/ MacWorld 1997 September / Macworld (1997-09).dmg / Serious Software / Cherwell Scientific Demos / pro Fit / pro Fit 5.0 demo (68k).sea / pro Fit 5.0 demo (68k) / Notes / Fitting differential equations / Example 1 / Nonlinear Decay function

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|00000000| 00 18 4e 6f 6e 6c 69 6e | 65 61 72 20 44 65 63 61 |..Nonlin|ear Deca|
|00000010| 79 20 66 75 6e 63 74 69 | 6f 6e 00 00 00 00 00 00 |y functi|on......|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 66 74 46 43 4e 4c 66 | 74 01 00 00 00 00 00 00 |.ftFCNLf|t.......|
|00000050| 00 00 00 00 00 0c f4 00 | 00 03 2f ad d6 32 a6 ad |........|../..2..|
|00000060| d6 32 a6 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.2......|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 bc d9 00 00 |........|........|
|00000080| 7b 0d 20 54 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |{. The f|ollowing|
|00000090| 20 61 72 65 20 74 68 65 | 20 66 6f 75 72 20 69 6e | are the| four in|
|000000a0| 74 65 67 72 61 74 69 6e | 67 20 66 75 6e 63 74 69 |tegratin|g functi|
|000000b0| 6f 6e 73 20 4e 6f 6e 6c | 69 6e 65 61 72 44 65 63 |ons Nonl|inearDec|
|000000c0| 61 79 2c 0d 20 4e 6f 6e | 6c 69 6e 65 61 72 44 65 |ay,. Non|linearDe|
|000000d0| 63 61 79 32 2c 20 4e 6f | 6e 6c 69 6e 65 61 72 44 |cay2, No|nlinearD|
|000000e0| 65 63 61 79 33 2c 20 4e | 6f 6e 6c 69 6e 65 61 72 |ecay3, N|onlinear|
|000000f0| 44 65 63 61 79 34 2c 20 | 77 68 69 63 68 20 61 72 |Decay4, |which ar|
|00000100| 65 0d 20 64 65 73 63 72 | 69 62 65 64 20 69 6e 20 |e. descr|ibed in |
|00000110| 74 68 65 20 54 65 63 68 | 4e 6f 74 65 20 22 46 69 |the Tech|Note "Fi|
|00000120| 74 74 69 6e 67 20 64 69 | 66 66 65 72 65 6e 74 69 |tting di|fferenti|
|00000130| 61 6c 20 65 71 75 61 74 | 69 6f 6e 73 22 2e 0d 7d |al equat|ions"..}|
|00000140| 0d 0d 0d 66 75 6e 63 74 | 69 6f 6e 20 4e 6f 6e 6c |...funct|ion Nonl|
|00000150| 69 6e 65 61 72 44 65 63 | 61 79 3b 0d 20 63 6f 6e |inearDec|ay;. con|
|00000160| 73 74 20 73 74 65 70 20 | 3d 20 30 2e 30 31 3b 0d |st step |= 0.01;.|
|00000170| 20 76 61 72 20 74 2c 20 | 64 74 3b 0d 62 65 67 69 | var t, |dt;.begi|
|00000180| 6e 0d 20 79 20 3a 3d 20 | 61 5b 34 5d 3b 20 20 20 |n. y := |a[4];   |
|00000190| 20 7b 73 74 61 72 74 20 | 76 61 6c 75 65 7d 0d 20 | {start |value}. |
|000001a0| 74 20 3a 3d 20 30 3b 20 | 20 20 20 20 20 20 7b 73 |t := 0; |      {s|
|000001b0| 74 61 72 74 20 74 69 6d | 65 7d 0d 20 64 74 20 3a |tart tim|e}. dt :|
|000001c0| 3d 20 73 74 65 70 3b 20 | 20 20 7b 73 74 65 70 20 |= step; |  {step |
|000001d0| 77 69 64 74 68 7d 0d 20 | 77 68 69 6c 65 20 74 20 |width}. |while t |
|000001e0| 3c 20 78 20 64 6f 0d 20 | 62 65 67 69 6e 0d 20 20 |< x do. |begin.  |
|000001f0| 20 69 66 20 74 2b 64 74 | 20 3e 20 78 20 74 68 65 | if t+dt| > x the|
|00000200| 6e 20 64 74 20 3a 3d 20 | 78 2d 74 3b 0d 20 20 20 |n dt := |x-t;.   |
|00000210| 79 20 3a 3d 20 79 20 2b | 20 64 74 2a 28 79 2a 28 |y := y +| dt*(y*(|
|00000220| 61 5b 31 5d 20 2b 20 79 | 2a 28 61 5b 32 5d 20 2b |a[1] + y|*(a[2] +|
|00000230| 20 79 2a 61 5b 33 5d 29 | 29 29 3b 0d 20 20 20 74 | y*a[3])|));.   t|
|00000240| 20 3a 3d 20 74 2b 64 74 | 3b 0d 20 65 6e 64 3b 0d | := t+dt|;. end;.|
|00000250| 65 6e 64 3b 0d 0d 0d 66 | 75 6e 63 74 69 6f 6e 20 |end;...f|unction |
|00000260| 4e 6f 6e 6c 69 6e 65 61 | 72 44 65 63 61 79 32 3b |Nonlinea|rDecay2;|
|00000270| 20 7b 52 75 6e 67 65 2d | 4b 75 74 74 61 7d 0d 20 | {Runge-|Kutta}. |
|00000280| 63 6f 6e 73 74 20 73 74 | 65 70 20 3d 20 30 2e 30 |const st|ep = 0.0|
|00000290| 35 3b 0d 20 76 61 72 20 | 74 2c 20 64 74 2c 20 6d |5;. var |t, dt, m|
|000002a0| 31 2c 20 6d 32 2c 20 6d | 33 2c 20 6d 34 2c 20 79 |1, m2, m|3, m4, y|
|000002b0| 31 3b 0d 62 65 67 69 6e | 0d 20 79 20 3a 3d 20 61 |1;.begin|. y := a|
|000002c0| 5b 34 5d 3b 20 20 20 20 | 7b 73 74 61 72 74 20 76 |[4];    |{start v|
|000002d0| 61 6c 75 65 7d 0d 20 74 | 20 3a 3d 20 30 3b 20 20 |alue}. t| := 0;  |
|000002e0| 20 20 20 20 20 7b 73 74 | 61 72 74 20 74 69 6d 65 |     {st|art time|
|000002f0| 7d 0d 20 64 74 20 3a 3d | 20 73 74 65 70 3b 20 20 |}. dt :=| step;  |
|00000300| 20 7b 73 74 65 70 20 77 | 69 64 74 68 7d 0d 20 77 | {step w|idth}. w|
|00000310| 68 69 6c 65 20 74 20 3c | 20 78 20 64 6f 0d 20 62 |hile t <| x do. b|
|00000320| 65 67 69 6e 0d 20 20 20 | 69 66 20 74 2b 64 74 20 |egin.   |if t+dt |
|00000330| 3e 20 78 20 74 68 65 6e | 20 64 74 20 3a 3d 20 78 |> x then| dt := x|
|00000340| 2d 74 3b 0d 20 20 20 6d | 31 20 3a 3d 20 79 2a 28 |-t;.   m|1 := y*(|
|00000350| 61 5b 31 5d 20 2b 20 79 | 2a 28 61 5b 32 5d 20 2b |a[1] + y|*(a[2] +|
|00000360| 20 79 2a 61 5b 33 5d 29 | 29 3b 0d 20 20 20 79 31 | y*a[3])|);.   y1|
|00000370| 20 3a 3d 20 79 20 2b 20 | 64 74 2a 6d 31 2a 30 2e | := y + |dt*m1*0.|
|00000380| 35 3b 0d 20 20 20 6d 32 | 20 3a 3d 20 79 31 2a 28 |5;.   m2| := y1*(|
|00000390| 61 5b 31 5d 20 2b 20 79 | 31 2a 28 61 5b 32 5d 20 |a[1] + y|1*(a[2] |
|000003a0| 2b 20 79 31 2a 61 5b 33 | 5d 29 29 3b 0d 20 20 20 |+ y1*a[3|]));.   |
|000003b0| 79 31 20 3a 3d 20 79 20 | 2b 20 64 74 2a 6d 32 2a |y1 := y |+ dt*m2*|
|000003c0| 30 2e 35 3b 0d 20 20 20 | 6d 33 20 3a 3d 20 79 31 |0.5;.   |m3 := y1|
|000003d0| 2a 28 61 5b 31 5d 20 2b | 20 79 31 2a 28 61 5b 32 |*(a[1] +| y1*(a[2|
|000003e0| 5d 20 2b 20 79 31 2a 61 | 5b 33 5d 29 29 3b 0d 20 |] + y1*a|[3]));. |
|000003f0| 20 20 79 31 20 3a 3d 20 | 79 20 2b 20 64 74 2a 6d |  y1 := |y + dt*m|
|00000400| 32 3b 0d 20 20 20 6d 34 | 20 3a 3d 20 79 31 2a 28 |2;.   m4| := y1*(|
|00000410| 61 5b 31 5d 20 2b 20 79 | 31 2a 28 61 5b 32 5d 20 |a[1] + y|1*(a[2] |
|00000420| 2b 20 79 31 2a 61 5b 33 | 5d 29 29 3b 0d 20 20 20 |+ y1*a[3|]));.   |
|00000430| 79 20 3a 3d 20 79 20 2b | 20 64 74 2a 28 6d 31 20 |y := y +| dt*(m1 |
|00000440| 2b 20 32 2a 6d 32 20 2b | 20 32 2a 6d 33 20 2b 20 |+ 2*m2 +| 2*m3 + |
|00000450| 6d 34 29 2f 36 3b 0d 20 | 20 20 74 20 3a 3d 20 74 |m4)/6;. |  t := t|
|00000460| 2b 64 74 3b 0d 20 65 6e | 64 3b 0d 65 6e 64 3b 0d |+dt;. en|d;.end;.|
|00000470| 0d 0d 66 75 6e 63 74 69 | 6f 6e 20 4e 6f 6e 6c 69 |..functi|on Nonli|
|00000480| 6e 65 61 72 44 65 63 61 | 79 33 3b 20 7b 74 65 6d |nearDeca|y3; {tem|
|00000490| 70 6f 72 61 72 79 20 73 | 74 6f 72 61 67 65 7d 0d |porary s|torage}.|
|000004a0| 20 63 6f 6e 73 74 20 73 | 74 65 70 20 3d 20 30 2e | const s|tep = 0.|
|000004b0| 30 31 3b 0d 20 76 61 72 | 20 74 2c 20 64 74 3b 0d |01;. var| t, dt;.|
|000004c0| 20 76 61 72 20 6c 61 73 | 74 58 2c 20 6c 61 73 74 | var las|tX, last|
|000004d0| 59 3b 0d 0d 70 72 6f 63 | 65 64 75 72 65 20 46 69 |Y;..proc|edure Fi|
|000004e0| 72 73 74 3b 20 7b 63 61 | 6c 6c 65 64 20 77 68 65 |rst; {ca|lled whe|
|000004f0| 6e 20 6c 61 73 74 58 2c | 20 6c 61 73 74 59 20 61 |n lastX,| lastY a|
|00000500| 72 65 20 73 74 61 6c 65 | 7d 0d 62 65 67 69 6e 0d |re stale|}.begin.|
|00000510| 20 6c 61 73 74 58 20 3a | 3d 20 30 3b 0d 20 6c 61 | lastX :|= 0;. la|
|00000520| 73 74 59 20 3a 3d 20 61 | 5b 34 5d 3b 0d 65 6e 64 |stY := a|[4];.end|
|00000530| 3b 0d 0d 62 65 67 69 6e | 0d 20 69 66 20 78 20 3e |;..begin|. if x >|
|00000540| 3d 20 6c 61 73 74 58 20 | 74 68 65 6e 20 62 65 67 |= lastX |then beg|
|00000550| 69 6e 0d 20 20 20 79 20 | 3a 3d 20 6c 61 73 74 59 |in.   y |:= lastY|
|00000560| 3b 20 20 20 20 7b 73 74 | 61 72 74 20 76 61 6c 75 |;    {st|art valu|
|00000570| 65 7d 0d 20 20 20 74 20 | 3a 3d 20 6c 61 73 74 58 |e}.   t |:= lastX|
|00000580| 3b 20 20 20 20 7b 73 74 | 61 72 74 20 74 69 6d 65 |;    {st|art time|
|00000590| 7d 0d 20 65 6e 64 0d 20 | 65 6c 73 65 20 62 65 67 |}. end. |else beg|
|000005a0| 69 6e 0d 20 20 20 79 20 | 3a 3d 20 61 5b 34 5d 3b |in.   y |:= a[4];|
|000005b0| 20 20 20 20 20 7b 73 74 | 61 72 74 20 76 61 6c 75 |     {st|art valu|
|000005c0| 65 7d 0d 20 20 20 74 20 | 3a 3d 20 30 3b 20 20 20 |e}.   t |:= 0;   |
|000005d0| 20 20 20 20 20 7b 73 74 | 61 72 74 20 74 69 6d 65 |     {st|art time|
|000005e0| 7d 0d 20 65 6e 64 3b 0d | 20 64 74 20 3a 3d 20 73 |}. end;.| dt := s|
|000005f0| 74 65 70 3b 20 20 20 7b | 73 74 65 70 20 77 69 64 |tep;   {|step wid|
|00000600| 74 68 7d 0d 20 77 68 69 | 6c 65 20 74 20 3c 20 78 |th}. whi|le t < x|
|00000610| 20 64 6f 0d 20 62 65 67 | 69 6e 0d 20 20 20 69 66 | do. beg|in.   if|
|00000620| 20 74 2b 64 74 20 3e 20 | 78 20 74 68 65 6e 20 64 | t+dt > |x then d|
|00000630| 74 20 3a 3d 20 78 2d 74 | 3b 0d 20 20 20 79 20 3a |t := x-t|;.   y :|
|00000640| 3d 20 79 20 2b 20 64 74 | 2a 28 79 2a 28 61 5b 31 |= y + dt|*(y*(a[1|
|00000650| 5d 20 2b 20 79 2a 28 61 | 5b 32 5d 20 2b 20 79 2a |] + y*(a|[2] + y*|
|00000660| 61 5b 33 5d 29 29 29 3b | 0d 20 20 20 74 20 3a 3d |a[3])));|.   t :=|
|00000670| 20 74 2b 64 74 3b 0d 20 | 65 6e 64 3b 0d 20 6c 61 | t+dt;. |end;. la|
|00000680| 73 74 58 20 3a 3d 20 78 | 3b 0d 20 6c 61 73 74 59 |stX := x|;. lastY|
|00000690| 20 3a 3d 20 79 3b 0d 65 | 6e 64 3b 0d 0d 0d 0d 66 | := y;.e|nd;....f|
|000006a0| 75 6e 63 74 69 6f 6e 20 | 4e 6f 6e 6c 69 6e 65 61 |unction |Nonlinea|
|000006b0| 72 44 65 63 61 79 34 3b | 20 7b 74 65 6d 70 6f 72 |rDecay4;| {tempor|
|000006c0| 61 72 79 20 73 74 6f 72 | 61 67 65 20 2f 20 44 65 |ary stor|age / De|
|000006d0| 72 69 76 61 74 69 76 65 | 73 7d 0d 20 63 6f 6e 73 |rivative|s}. cons|
|000006e0| 74 20 73 74 65 70 20 3d | 20 30 2e 30 31 3b 0d 20 |t step =| 0.01;. |
|000006f0| 20 20 20 20 20 20 65 70 | 73 69 6c 6f 6e 20 3d 20 |      ep|silon = |
|00000700| 31 65 2d 38 3b 20 7b 61 | 20 73 6d 61 6c 6c 20 64 |1e-8; {a| small d|
|00000710| 65 76 69 61 74 69 6f 6e | 20 66 6f 72 20 61 6c 6c |eviation| for all|
|00000720| 20 70 61 72 61 6d 73 7d | 0d 20 76 61 72 20 6c 61 | params}|. var la|
|00000730| 73 74 58 30 2c 20 6c 61 | 73 74 59 30 2c 20 6c 61 |stX0, la|stY0, la|
|00000740| 73 74 58 31 2c 20 6c 61 | 73 74 59 31 2c 20 6c 61 |stX1, la|stY1, la|
|00000750| 73 74 58 32 2c 20 6c 61 | 73 74 59 32 2c 20 0d 20 |stX2, la|stY2, . |
|00000760| 20 20 20 20 6c 61 73 74 | 58 33 2c 20 6c 61 73 74 |    last|X3, last|
|00000770| 59 33 2c 20 6c 61 73 74 | 58 34 2c 20 6c 61 73 74 |Y3, last|X4, last|
|00000780| 59 34 3b 0d 0d 0d 66 75 | 6e 63 74 69 6f 6e 20 49 |Y4;...fu|nction I|
|00000790| 6e 74 65 67 72 61 74 65 | 28 6c 61 73 74 58 2c 20 |ntegrate|(lastX, |
|000007a0| 6c 61 73 74 59 2c 20 78 | 56 61 6c 2c 20 61 31 2c |lastY, x|Val, a1,|
|000007b0| 20 61 32 2c 20 61 33 2c | 20 61 34 29 3b 0d 20 7b | a2, a3,| a4);. {|
|000007c0| 72 75 6e 73 20 6f 6e 65 | 20 69 6e 74 65 67 72 61 |runs one| integra|
|000007d0| 74 69 6f 6e 7d 0d 20 76 | 61 72 20 79 56 61 6c 2c |tion}. v|ar yVal,|
|000007e0| 20 74 2c 20 64 74 3b 0d | 62 65 67 69 6e 0d 20 69 | t, dt;.|begin. i|
|000007f0| 66 20 78 56 61 6c 20 3e | 3d 20 6c 61 73 74 58 20 |f xVal >|= lastX |
|00000800| 74 68 65 6e 20 62 65 67 | 69 6e 0d 20 20 20 79 56 |then beg|in.   yV|
|00000810| 61 6c 20 3a 3d 20 6c 61 | 73 74 59 3b 20 20 20 20 |al := la|stY;    |
|00000820| 7b 73 74 61 72 74 20 76 | 61 6c 75 65 7d 0d 20 20 |{start v|alue}.  |
|00000830| 20 74 20 3a 3d 20 6c 61 | 73 74 58 3b 20 20 20 20 | t := la|stX;    |
|00000840| 7b 73 74 61 72 74 20 74 | 69 6d 65 7d 0d 20 65 6e |{start t|ime}. en|
|00000850| 64 0d 20 65 6c 73 65 20 | 62 65 67 69 6e 0d 20 20 |d. else |begin.  |
|00000860| 20 79 56 61 6c 20 3a 3d | 20 61 34 3b 20 20 20 20 | yVal :=| a4;    |
|00000870| 20 20 20 7b 73 74 61 72 | 74 20 76 61 6c 75 65 7d |   {star|t value}|
|00000880| 0d 20 20 20 74 20 3a 3d | 20 30 3b 20 20 20 20 20 |.   t :=| 0;     |
|00000890| 20 20 20 7b 73 74 61 72 | 74 20 74 69 6d 65 7d 0d |   {star|t time}.|
|000008a0| 20 65 6e 64 3b 0d 20 64 | 74 20 3a 3d 20 73 74 65 | end;. d|t := ste|
|000008b0| 70 3b 20 20 20 7b 73 74 | 65 70 20 77 69 64 74 68 |p;   {st|ep width|
|000008c0| 7d 0d 20 77 68 69 6c 65 | 20 74 20 3c 20 78 56 61 |}. while| t < xVa|
|000008d0| 6c 20 64 6f 0d 20 62 65 | 67 69 6e 0d 20 20 20 69 |l do. be|gin.   i|
|000008e0| 66 20 74 2b 64 74 20 3e | 20 78 56 61 6c 20 74 68 |f t+dt >| xVal th|
|000008f0| 65 6e 20 64 74 20 3a 3d | 20 78 56 61 6c 2d 74 3b |en dt :=| xVal-t;|
|00000900| 0d 20 20 20 79 56 61 6c | 20 3a 3d 20 79 56 61 6c |.   yVal| := yVal|
|00000910| 20 2b 20 64 74 2a 28 79 | 56 61 6c 2a 28 61 31 20 | + dt*(y|Val*(a1 |
|00000920| 2b 20 79 56 61 6c 2a 28 | 61 32 20 2b 20 79 56 61 |+ yVal*(|a2 + yVa|
|00000930| 6c 2a 61 33 29 29 29 3b | 0d 20 20 20 74 20 3a 3d |l*a3)));|.   t :=|
|00000940| 20 74 2b 64 74 3b 0d 20 | 65 6e 64 3b 0d 20 49 6e | t+dt;. |end;. In|
|00000950| 74 65 67 72 61 74 65 20 | 3a 3d 20 79 56 61 6c 3b |tegrate |:= yVal;|
|00000960| 0d 65 6e 64 3b 0d 0d 0d | 70 72 6f 63 65 64 75 72 |.end;...|procedur|
|00000970| 65 20 46 69 72 73 74 3b | 20 7b 63 61 6c 6c 65 64 |e First;| {called|
|00000980| 20 77 68 65 6e 20 6c 61 | 73 74 58 2c 20 6c 61 73 | when la|stX, las|
|00000990| 74 59 20 61 72 65 20 73 | 74 61 6c 65 7d 0d 62 65 |tY are s|tale}.be|
|000009a0| 67 69 6e 0d 20 6c 61 73 | 74 58 30 20 3a 3d 20 30 |gin. las|tX0 := 0|
|000009b0| 3b 20 6c 61 73 74 59 30 | 20 3a 3d 20 61 5b 34 5d |; lastY0| := a[4]|
|000009c0| 3b 0d 20 6c 61 73 74 58 | 31 20 3a 3d 20 30 3b 20 |;. lastX|1 := 0; |
|000009d0| 6c 61 73 74 59 31 20 3a | 3d 20 61 5b 34 5d 3b 0d |lastY1 :|= a[4];.|
|000009e0| 20 6c 61 73 74 58 32 20 | 3a 3d 20 30 3b 20 6c 61 | lastX2 |:= 0; la|
|000009f0| 73 74 59 32 20 3a 3d 20 | 61 5b 34 5d 3b 0d 20 6c |stY2 := |a[4];. l|
|00000a00| 61 73 74 58 33 20 3a 3d | 20 30 3b 20 6c 61 73 74 |astX3 :=| 0; last|
|00000a10| 59 33 20 3a 3d 20 61 5b | 34 5d 3b 0d 20 6c 61 73 |Y3 := a[|4];. las|
|00000a20| 74 58 34 20 3a 3d 20 30 | 3b 20 6c 61 73 74 59 34 |tX4 := 0|; lastY4|
|00000a30| 20 3a 3d 20 61 5b 34 5d | 2b 65 70 73 69 6c 6f 6e | := a[4]|+epsilon|
|00000a40| 3b 0d 65 6e 64 3b 0d 0d | 70 72 6f 63 65 64 75 72 |;.end;..|procedur|
|00000a50| 65 20 44 65 72 69 76 61 | 74 69 76 65 73 3b 0d 20 |e Deriva|tives;. |
|00000a60| 20 76 61 72 20 79 56 61 | 6c 2c 20 79 56 61 6c 31 | var yVa|l, yVal1|
|00000a70| 3b 0d 62 65 67 69 6e 0d | 20 20 79 56 61 6c 20 3a |;.begin.|  yVal :|
|00000a80| 3d 20 49 6e 74 65 67 72 | 61 74 65 28 6c 61 73 74 |= Integr|ate(last|
|00000a90| 58 30 2c 20 6c 61 73 74 | 59 30 2c 20 78 2c 20 61 |X0, last|Y0, x, a|
|00000aa0| 5b 31 5d 2c 20 61 5b 32 | 5d 2c 20 61 5b 33 5d 2c |[1], a[2|], a[3],|
|00000ab0| 20 61 5b 34 5d 29 3b 0d | 20 20 6c 61 73 74 58 30 | a[4]);.|  lastX0|
|00000ac0| 20 3a 3d 20 78 3b 20 6c | 61 73 74 59 30 20 3a 3d | := x; l|astY0 :=|
|00000ad0| 20 79 56 61 6c 3b 0d 0d | 20 20 79 56 61 6c 31 20 | yVal;..|  yVal1 |
|00000ae0| 3a 3d 20 49 6e 74 65 67 | 72 61 74 65 28 6c 61 73 |:= Integ|rate(las|
|00000af0| 74 58 31 2c 20 6c 61 73 | 74 59 31 2c 20 78 2c 20 |tX1, las|tY1, x, |
|00000b00| 61 5b 31 5d 2b 65 70 73 | 69 6c 6f 6e 2c 20 61 5b |a[1]+eps|ilon, a[|
|00000b10| 32 5d 2c 20 61 5b 33 5d | 2c 20 61 5b 34 5d 29 3b |2], a[3]|, a[4]);|
|00000b20| 0d 20 20 6c 61 73 74 58 | 31 20 3a 3d 20 78 3b 20 |.  lastX|1 := x; |
|00000b30| 6c 61 73 74 59 31 20 3a | 3d 20 79 56 61 6c 31 3b |lastY1 :|= yVal1;|
|00000b40| 0d 20 20 64 79 64 61 5b | 31 5d 20 3a 3d 20 28 79 |.  dyda[|1] := (y|
|00000b50| 56 61 6c 31 2d 79 56 61 | 6c 29 2f 65 70 73 69 6c |Val1-yVa|l)/epsil|
|00000b60| 6f 6e 3b 0d 0d 20 20 79 | 56 61 6c 31 20 3a 3d 20 |on;..  y|Val1 := |
|00000b70| 49 6e 74 65 67 72 61 74 | 65 28 6c 61 73 74 58 32 |Integrat|e(lastX2|
|00000b80| 2c 20 6c 61 73 74 59 32 | 2c 20 78 2c 20 61 5b 31 |, lastY2|, x, a[1|
|00000b90| 5d 2c 20 61 5b 32 5d 2b | 65 70 73 69 6c 6f 6e 2c |], a[2]+|epsilon,|
|00000ba0| 20 61 5b 33 5d 2c 20 61 | 5b 34 5d 29 3b 0d 20 20 | a[3], a|[4]);.  |
|00000bb0| 6c 61 73 74 58 32 20 3a | 3d 20 78 3b 20 6c 61 73 |lastX2 :|= x; las|
|00000bc0| 74 59 32 20 3a 3d 20 79 | 56 61 6c 31 3b 0d 20 20 |tY2 := y|Val1;.  |
|00000bd0| 64 79 64 61 5b 32 5d 20 | 3a 3d 20 28 79 56 61 6c |dyda[2] |:= (yVal|
|00000be0| 31 2d 79 56 61 6c 29 2f | 65 70 73 69 6c 6f 6e 3b |1-yVal)/|epsilon;|
|00000bf0| 0d 0d 20 20 79 56 61 6c | 31 20 3a 3d 20 49 6e 74 |..  yVal|1 := Int|
|00000c00| 65 67 72 61 74 65 28 6c | 61 73 74 58 33 2c 20 6c |egrate(l|astX3, l|
|00000c10| 61 73 74 59 33 2c 20 78 | 2c 20 61 5b 31 5d 2c 20 |astY3, x|, a[1], |
|00000c20| 61 5b 32 5d 2c 20 61 5b | 33 5d 2b 65 70 73 69 6c |a[2], a[|3]+epsil|
|00000c30| 6f 6e 2c 20 61 5b 34 5d | 29 3b 0d 20 20 6c 61 73 |on, a[4]|);.  las|
|00000c40| 74 58 33 20 3a 3d 20 78 | 3b 20 6c 61 73 74 59 33 |tX3 := x|; lastY3|
|00000c50| 20 3a 3d 20 79 56 61 6c | 31 3b 0d 20 20 64 79 64 | := yVal|1;.  dyd|
|00000c60| 61 5b 33 5d 20 3a 3d 20 | 28 79 56 61 6c 31 2d 79 |a[3] := |(yVal1-y|
|00000c70| 56 61 6c 29 2f 65 70 73 | 69 6c 6f 6e 3b 0d 0d 20 |Val)/eps|ilon;.. |
|00000c80| 20 79 56 61 6c 31 20 3a | 3d 20 49 6e 74 65 67 72 | yVal1 :|= Integr|
|00000c90| 61 74 65 28 6c 61 73 74 | 58 34 2c 20 6c 61 73 74 |ate(last|X4, last|
|00000ca0| 59 34 2c 20 78 2c 20 61 | 5b 31 5d 2c 20 61 5b 32 |Y4, x, a|[1], a[2|
|00000cb0| 5d 2c 20 61 5b 33 5d 2c | 20 61 5b 34 5d 2b 65 70 |], a[3],| a[4]+ep|
|00000cc0| 73 69 6c 6f 6e 29 3b 0d | 20 20 6c 61 73 74 58 34 |silon);.|  lastX4|
|00000cd0| 20 3a 3d 20 78 3b 20 6c | 61 73 74 59 34 20 3a 3d | := x; l|astY4 :=|
|00000ce0| 20 79 56 61 6c 31 3b 0d | 20 20 64 79 64 61 5b 34 | yVal1;.|  dyda[4|
|00000cf0| 5d 20 3a 3d 20 28 79 56 | 61 6c 31 2d 79 56 61 6c |] := (yV|al1-yVal|
|00000d00| 29 2f 65 70 73 69 6c 6f | 6e 3b 0d 65 6e 64 3b 0d |)/epsilo|n;.end;.|
|00000d10| 0d 62 65 67 69 6e 0d 20 | 79 20 3a 3d 20 49 6e 74 |.begin. |y := Int|
|00000d20| 65 67 72 61 74 65 28 6c | 61 73 74 58 30 2c 20 6c |egrate(l|astX0, l|
|00000d30| 61 73 74 59 30 2c 20 78 | 2c 20 61 5b 31 5d 2c 20 |astY0, x|, a[1], |
|00000d40| 61 5b 32 5d 2c 20 61 5b | 33 5d 2c 20 61 5b 34 5d |a[2], a[|3], a[4]|
|00000d50| 29 3b 0d 20 6c 61 73 74 | 58 30 20 3a 3d 20 78 3b |);. last|X0 := x;|
|00000d60| 0d 20 6c 61 73 74 59 30 | 20 3a 3d 20 79 3b 0d 65 |. lastY0| := y;.e|
|00000d70| 6e 64 3b 0d 00 00 00 00 | 00 00 00 00 00 00 00 00 |nd;.....|........|
|00000d80| 00 00 01 00 00 00 02 b9 | 00 00 01 b9 00 00 00 76 |........|.......v|
|00000d90| 61 72 44 65 63 61 79 3b | 0d 20 63 6f 6e 73 74 20 |arDecay;|. const |
|00000da0| 73 74 65 70 20 3d 20 30 | 2e 30 31 3b 0d 20 76 61 |step = 0|.01;. va|
|00000db0| 18 4e 6f 6e 6c 69 6e 65 | 61 72 20 44 65 63 61 79 |.Nonline|ar Decay|
|00000dc0| 20 66 75 6e 63 74 69 6f | 6e 6e 02 00 00 00 66 74 | functio|nn....ft|
|00000dd0| 00 00 66 74 46 43 4e 4c | 66 74 01 00 00 28 00 00 |..ftFCNL|ft...(..|
|00000de0| 00 00 00 00 00 00 00 00 | 00 00 80 00 00 00 00 00 |........|........|
|00000df0| 00 00 ad d5 bf 7d 00 00 | 0c f4 00 00 03 2f 20 73 |.....}..|...../ s|
|00000e00| 74 65 70 3b 20 20 20 7b | 73 74 65 70 20 77 69 64 |tep;   {|step wid|
|00000e10| 74 68 7d 0d 20 77 68 69 | 6c 65 20 74 20 3c 20 78 |th}. whi|le t < x|
|00000e20| 20 64 6f 0d 20 62 65 67 | 69 6e 0d 20 20 20 69 66 | do. beg|in.   if|
|00000e30| 20 74 2b 64 74 20 3e 20 | 78 20 74 68 65 6e 20 64 | t+dt > |x then d|
|00000e40| 74 20 3a 3d 20 78 2d 74 | 3b 0d 20 20 20 79 20 3a |t := x-t|;.   y :|
|00000e50| 3d 20 79 20 2b 20 64 74 | 2a 28 79 2a 28 61 5b 31 |= y + dt|*(y*(a[1|
|00000e60| 5d 20 2b 20 79 2a 28 61 | 5b 32 5d 20 2b 20 79 2a |] + y*(a|[2] + y*|
|00000e70| 61 5b 33 5d 29 29 29 3b | 0d 20 20 20 74 20 3a 3d |a[3])));|.   t :=|
|00000e80| 00 00 00 08 00 7b 00 29 | 01 ae 02 22 00 00 01 06 |.....{.)|..."....|
|00000e90| 00 04 00 09 00 00 06 4d | 6f 6e 61 63 6f 28 40 a1 |.......M|onaco(@.|
|00000ea0| 27 a0 00 4e 3f 20 00 81 | 00 00 00 01 d9 94 fe 00 |'..N? ..|........|
|00000eb0| 10 00 02 68 a0 dc 02 68 | 9f 30 00 02 a2 04 00 0b |...h...h|.0......|
|00000ec0| 00 06 00 0b 00 06 00 01 | 9f 20 02 43 0b 38 00 00 |........|. .C.8..|
|00000ed0| 00 00 00 00 00 00 02 68 | a0 40 00 0b a8 44 03 3e |.......h|.@...D.>|
|00000ee0| 52 a8 00 00 00 02 00 2a | 00 11 02 42 b5 30 00 0d |R......*|...B.0..|
|00000ef0| 73 50 02 68 9f 98 00 0d | 73 5c 02 43 e5 50 02 43 |sP.h....|s\.C.P.C|
|00000f00| 0b da 00 00 00 01 00 03 | c8 90 00 04 eb b0 00 03 |........|........|
|00000f10| c8 90 00 00 00 00 02 68 | 9f a0 00 19 61 10 00 14 |.......h|....a...|
|00000f20| d8 38 00 19 61 30 02 68 | 9f a0 00 18 c3 2c 00 14 |.8..a0.h|.....,..|
|00000f30| d1 b4 00 49 82 60 02 68 | 9f a0 00 18 c3 2c 00 0d |...I.`.h|.....,..|
|00000f40| 73 5c 00 0d 73 50 02 68 | 9f d0 00 18 c3 2c 00 1a |s\..sP.h|.....,..|
|00000f50| 14 5c 00 00 03 e1 02 68 | 9f b0 00 0d 73 74 00 11 |.\.....h|....st..|
|00000f60| 47 c8 00 04 eb b0 00 00 | 64 d0 00 01 2f a4 00 00 |G.......|d.../...|
|00000f70| 00 00 00 0b ae 60 02 43 | 2e fa 00 19 61 10 07 80 |.....`.C|....a...|
|00000f80| 03 80 00 00 00 00 02 68 | a0 00 02 68 9f f0 00 14 |.......h|...h....|
|00000f90| cf 48 00 00 00 02 00 00 | 00 10 00 00 00 00 00 00 |.H......|........|
|00000fa0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 04 00 00 |........|........|
|00000fb0| 00 01 00 00 00 78 00 03 | 00 00 00 48 00 48 00 00 |.....x..|...H.H..|
|00000fc0| 00 00 03 0d 02 1a ff e2 | ff e3 03 2c 02 36 03 47 |........|...,.6.G|
|00000fd0| 05 7b 03 e0 00 02 00 00 | 00 48 00 48 00 00 00 00 |.{......|.H.H....|
|00000fe0| 02 d8 02 28 00 01 00 00 | 00 64 00 00 00 01 00 03 |...(....|.d......|
|00000ff0| 03 03 00 ff 00 01 27 0f | 00 01 00 01 00 00 00 00 |......'.|........|
|00001000| 00 00 00 00 00 00 00 00 | 60 08 00 19 01 90 00 00 |........|`.......|
|00001010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 01 00 00 |........|........|
|00001020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001030| 00 07 06 70 72 6f 46 69 | 74 00 00 01 00 00 00 02 |...proFi|t.......|
|00001040| b9 00 00 01 b9 00 00 00 | 76 02 43 42 4c 24 5c 00 |........|v.CBL$\.|
|00001050| 00 00 1c 00 76 00 01 66 | 49 4e 46 00 04 00 12 53 |....v..f|INF....S|
|00001060| 54 52 20 00 00 00 4e 00 | 81 ff ff 00 00 00 00 02 |TR ...N.|........|
|00001070| 43 38 f4 00 82 ff ff 00 | 00 00 0c 02 43 33 9c 00 |C8......|....C3..|
|00001080| 83 ff ff 00 00 01 16 02 | 43 38 94 00 85 ff ff 00 |........|C8......|
|00001090| 00 01 2a 02 43 38 d4 00 | 84 ff ff 00 00 01 32 02 |..*.C8..|......2.|
|000010a0| 41 66 78 bf f4 ff ff 00 | 00 01 ae 02 43 35 a0 00 |Afx.....|....C5..|
|000010b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000010c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000010d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000010e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000010f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+