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Odkazy

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with(NumericalMethods);

Digits:=25;

ODE:=diff(y(x),x)=-2*x*y(x);

IC:=y(0)=1;

sol:=exp(-x^2);

h:=0.05;

k:=0.005;

K:=0.0005;

Eh1:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=h, solution=sol, output=plot);

Ek1:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=k, solution=sol, output=plot);

EK1:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,3], stepsize=K, solution=sol, output=plot);

q11:=ln(Eh1/Ek1)/ln(h/k);

q12:=ln(Ek1/EK1)/ln(k/K);

Eh2:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=h, solution=sol, output=plot)

Ek2:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=k, solution=sol, output=plot);

EK2:=ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..3, method=[taylor,4], stepsize=K, solution=sol, output=plot)

q21 := ln(Eh2/Ek2)/ln(h/k);

q22 := ln(Ek2/EK2)/ln(k/K);

h := 0.5e-1;

k := 0.5e-2;

K := 0.5e-3

Eh1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,3],stepsize = h,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,3],stepsize = h,solution = sol,output = plot);

Ek1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,3],stepsize = k,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,3],stepsize = k,solution = sol,output = plot);

EK1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,3],stepsize = K,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,3],stepsize = K,solution = sol,output = plot);

q11 := ln(Eh1/Ek1)/ln(h/k);

q12 := ln(Ek1/EK1)/ln(k/K);

q13 := ln(Eh1/EK1)/ln(h/K);

Eh1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,4],stepsize = h,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,4],stepsize = h,solution = sol,output = plot);

Ek1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,4],stepsize = k,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,4],stepsize = k,solution = sol,output = plot);

EK1 := ODENumeric(ODE,yinit=[1],x=0..8,method=[taylor,4],stepsize = K,solution = sol,output = totalerror);

ODENumeric(ODE,yinit=1,x=0..8,method=[taylor,4],stepsize = K,solution = sol,output = plot);

q21 := ln(Eh2/Ek2)/ln(h/k);

q22 := ln(Ek2/EK2)/ln(k/K);

q23 := ln(Eh2/EK2)/ln(h/K);

Eh1:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=h, solution=sol, output=plot);

Ek1:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=k, solution=sol, output=plot);

EK1:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,3], stepsize=K, solution=sol, output=plot);

q11:=ln(Eh1/Ek1)/ln(h/k);

q12:=ln(Ek1/EK1)/ln(k/K);

Eh2:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=h, solution=sol, output=plot);

Ek2:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=k, solution=sol, output=plot);

EK2:=ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..8, method=[taylor,4], stepsize=K, solution=sol, output=plot);

q21 := ln(Eh2/Ek2)/ln(h/k);

q22 := ln(Ek2/EK2)/ln(k/K);

Eh1:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=h, solution=sol, output=plot);

Ek1:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=k, solution=sol, output=plot);

EK1:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,3], stepsize=K, solution=sol, output=plot);

q11:=ln(Eh1/Ek1)/ln(h/k);

q12:=ln(Ek1/EK1)/ln(k/K);

Eh2:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=h, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=h, solution=sol, output=plot);

Ek2:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=k, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=k, solution=sol, output=plot);

EK2:=ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=K, solution=sol, output=totalerror);

ODENumeric(ODE, yinit=[1], x=0..1, method=[taylor,4], stepsize=K, solution=sol, output=plot);

q21 := ln(Eh2/Ek2)/ln(h/k);

q22 := ln(Ek2/EK2)/ln(k/K);

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Petr Dočekal

Petr.Docekal.hdcr@seznam.cz

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