Solve the ODE x' = x - t^2 +1 subject to x(0)=.5 on the interval [0,2]g:=x-t^2+1;

NiM+SSJnRzYiLChJInhHRiUiIiIqJEkidEdGJSIiIyEiIkYoRig=

f:=unapply(g,t,x);

NiM+SSJmRzYiZio2JEkidEdGJUkieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCg5JSIiIiokOSQiIiMhIiJGL0YvRiVGJUYl

n:=100;

NiM+SSJuRzYiIiQrIg==

t[0]:=0;

NiM+JkkidEc2IjYjIiIhRig=

h:=(2-0)/n;

NiM+SSJoRzYiIyIiIiIjXQ==

x[0]:=0.5;

NiM+JkkieEc2IjYjIiIhJCIiJiEiIg==

c[1]:=-10;

NiM+JkkiY0c2IjYjIiIiISM1

c[2]:=1-c[1];

NiM+JkkiY0c2IjYjIiIjIiM2

c[3]:=1/(2*c[2]);

NiM+JkkiY0c2IjYjIiIkIyIiIiIjQQ==

c[4]:=1/(2*c[2]);

NiM+JkkiY0c2IjYjIiIlIyIiIiIjQQ==

for i from 0 by 1 to n-1 do F1:=h*f(t[i],x[i]); F2:=h*f(t[i]+c[3]*h,x[i]+c[4]*F1); x[i+1]:=x[i]+c[1]*F1+c[2]*F2; t[i+1]:=t[i]+hod:ode:=diff(y(z),z)=y(z)-z^2+1;

NiM+SSRvZGVHNiIvLUklZGlmZkdJKnByb3RlY3RlZEdGKTYkLUkieUdGJTYjSSJ6R0YlRi4sKEYrIiIiKiRGLiIiIyEiIkYwRjA=

ic:=y(0)=0.5;

NiM+SSNpY0c2Ii8tSSJ5R0YlNiMiIiEkIiImISIi

silly:=dsolve({ode,ic},y(z));

NiM+SSZzaWxseUc2Ii8tSSJ5R0YlNiNJInpHRiUsJiokLCZGKiIiIkYuRi4iIiNGLi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YzSShfc3lzbGliR0YlRikjISIiRi8=

sol:=unapply(silly2,z);

NiM+SSRzb2xHNiJmKjYjSSJ6R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiokLCY5JCIiIkYwRjAiIiNGMC1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y1SShfc3lzbGliR0YlNiNGLyMhIiJGMUYlRiVGJQ==

sol(0);

NiMjIiIiIiIj

for j from 0 by 1 to n do print("step=",j,"t=",0+j*h,"ABSerror=",abs(x[j]-evalf(sol(0+j*h))));od;

NihRJnN0ZXA9NiIiIiFRI3Q9RiRGJVEqQUJTZXJyb3I9RiQkRiVGJQ==NihRJnN0ZXA9NiIiIiJRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCIlIylbISM1NihRJnN0ZXA9NiIiIiNRI3Q9RiQjIiIiIiNEUSpBQlNlcnJvcj1GJCQiJSgqKiohIzU=NihRJnN0ZXA9NiIiIiRRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImZGAiISM1NihRJnN0ZXA9NiIiIiVRI3Q9RiQjIiIjIiNEUSpBQlNlcnJvcj1GJCQiJmo0IyEjNQ==NihRJnN0ZXA9NiIiIiZRI3Q9RiQjIiIiIiM1USpBQlNlcnJvcj1GJCQiJkNvIyEjNQ==NihRJnN0ZXA9NiIiIidRI3Q9RiQjIiIkIiNEUSpBQlNlcnJvcj1GJCQiJmNIJCEjNQ==NihRJnN0ZXA9NiIiIihRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImYiRSISM1NihRJnN0ZXA9NiIiIilRI3Q9RiQjIiIlIiNEUSpBQlNlcnJvcj1GJCQiJlFnJSEjNQ==NihRJnN0ZXA9NiIiIipRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImOEkmISM1NihRJnN0ZXA9NiIiIzVRI3Q9RiQjIiIiIiImUSpBQlNlcnJvcj1GJCQiJidHZyEjNQ==NihRJnN0ZXA9NiIiIzZRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImcXknISM1NihRJnN0ZXA9NiIiIzdRI3Q9RiQjIiInIiNEUSpBQlNlcnJvcj1GJCQiJm9kKCEjNQ==NihRJnN0ZXA9NiIiIzhRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImLVMpISM1NihRJnN0ZXA9NiIiIzlRI3Q9RiQjIiIoIiNEUSpBQlNlcnJvcj1GJCQiJm1EKiEjNQ==NihRJnN0ZXA9NiIiIzpRI3Q9RiQjIiIkIiM1USpBQlNlcnJvcj1GJCQiJlwsIiEiKg==NihRJnN0ZXA9NiIiIztRI3Q9RiQjIiIpIiNEUSpBQlNlcnJvcj1GJCQiJnc1IiEiKg==NihRJnN0ZXA9NiIiIzxRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImVD8iISIqNihRJnN0ZXA9NiIiIz1RI3Q9RiQjIiIqIiNEUSpBQlNlcnJvcj1GJCQiJldJIiEiKg==NihRJnN0ZXA9NiIiIz5RI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImJjM5ISIqNihRJnN0ZXA9NiIiIz9RI3Q9RiQjIiIjIiImUSpBQlNlcnJvcj1GJCQiJm9eIiEiKg==NihRJnN0ZXA9NiIiI0BRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImI0g7ISIqNihRJnN0ZXA9NiIiI0FRI3Q9RiQjIiM2IiNEUSpBQlNlcnJvcj1GJCQiJmd1IiEiKg==NihRJnN0ZXA9NiIiI0JRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImcSc9ISIqNihRJnN0ZXA9NiIiI0NRI3Q9RiQjIiM3IiNEUSpBQlNlcnJvcj1GJCQiJkYqPiEiKg==NihRJnN0ZXA9NiIiI0RRI3Q9RiQjIiIiIiIjUSpBQlNlcnJvcj1GJCQiJko3IyEiKg==NihRJnN0ZXA9NiIiI0VRI3Q9RiQjIiM4IiNEUSpBQlNlcnJvcj1GJCQiJiNlQSEiKg==NihRJnN0ZXA9NiIiI0ZRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImJClSIyEiKg==NihRJnN0ZXA9NiIiI0dRI3Q9RiQjIiM5IiNEUSpBQlNlcnJvcj1GJCQiJk9hIyEiKg==NihRJnN0ZXA9NiIiI0hRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImVXAjISIqNihRJnN0ZXA9NiIiI0lRI3Q9RiQjIiIkIiImUSpBQlNlcnJvcj1GJCQiJismRyEiKg==NihRJnN0ZXA9NiIiI0pRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImOiwkISIqNihRJnN0ZXA9NiIiI0tRI3Q9RiQjIiM7IiNEUSpBQlNlcnJvcj1GJCQiJih5SiEiKg==NihRJnN0ZXA9NiIiI0xRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImPU4kISIqNihRJnN0ZXA9NiIiI01RI3Q9RiQjIiM8IiNEUSpBQlNlcnJvcj1GJCQiJjVgJCEiKg==NihRJnN0ZXA9NiIiI05RI3Q9RiQjIiIoIiM1USpBQlNlcnJvcj1GJCQiJmtyJCEiKg==NihRJnN0ZXA9NiIiI09RI3Q9RiQjIiM9IiNEUSpBQlNlcnJvcj1GJCQiJiMzUiEiKg==NihRJnN0ZXA9NiIiI1BRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImbDUlISIqNihRJnN0ZXA9NiIiI1FRI3Q9RiQjIiM+IiNEUSpBQlNlcnJvcj1GJCQiJjxKJSEiKg==NihRJnN0ZXA9NiIiI1JRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImUV8lISIqNihRJnN0ZXA9NiIiI1NRI3Q9RiQjIiIlIiImUSpBQlNlcnJvcj1GJCQiJkt1JSEiKg==NihRJnN0ZXA9NiIiI1RRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImKnBcISIqNihRJnN0ZXA9NiIiI1VRI3Q9RiQjIiNAIiNEUSpBQlNlcnJvcj1GJCQiJlU/JiEiKg==NihRJnN0ZXA9NiIiI1ZRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCIma1cmISIqNihRJnN0ZXA9NiIiI1dRI3Q9RiQjIiNBIiNEUSpBQlNlcnJvcj1GJCQiJm1wJiEiKg==NihRJnN0ZXA9NiIiI1hRI3Q9RiQjIiIqIiM1USpBQlNlcnJvcj1GJCQiJl0mZiEiKg==NihRJnN0ZXA9NiIiI1lRI3Q9RiQjIiNCIiNEUSpBQlNlcnJvcj1GJCQiJj1BJyEiKg==NihRJnN0ZXA9NiIiI1pRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImdVwnISIqNihRJnN0ZXA9NiIiI1tRI3Q9RiQjIiNDIiNEUSpBQlNlcnJvcj1GJCQiJj55JyEiKg==NihRJnN0ZXA9NiIiI1xRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImZDIoISIqNihRJnN0ZXA9NiIiI11RI3Q9RiQiIiJRKkFCU2Vycm9yPUYkJCImIXp0ISIqNihRJnN0ZXA9NiIiI15RI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImP3AoISIqNihRJnN0ZXA9NiIiI19RI3Q9RiQjIiNFIiNEUSpBQlNlcnJvcj1GJCQiJlwsKSEiKg==NihRJnN0ZXA9NiIiI2BRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImI1skKSEiKg==NihRJnN0ZXA9NiIiI2FRI3Q9RiQjIiNGIiNEUSpBQlNlcnJvcj1GJCQiJkBwKSEiKg==NihRJnN0ZXA9NiIiI2JRI3Q9RiQjIiM2IiM1USpBQlNlcnJvcj1GJCQiJm4vKiEiKg==NihRJnN0ZXA9NiIiI2NRI3Q9RiQjIiNHIiNEUSpBQlNlcnJvcj1GJCQiJkVUKiEiKg==NihRJnN0ZXA9NiIiI2RRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCImKSp5KiEiKg==NihRJnN0ZXA9NiIiI2VRI3Q9RiQjIiNIIiNEUSpBQlNlcnJvcj1GJCQiJyp5LCIhIio=NihRJnN0ZXA9NiIiI2ZRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInLWU1ISIqNihRJnN0ZXA9NiIiI2dRI3Q9RiQjIiInIiImUSpBQlNlcnJvcj1GJCQiJ1EqNCIhIio=NihRJnN0ZXA9NiIiI2hRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInLFU2ISIqNihRJnN0ZXA9NiIiI2lRI3Q9RiQjIiNKIiNEUSpBQlNlcnJvcj1GJCQiJyZmPSIhIio=NihRJnN0ZXA9NiIiI2pRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInQ0o3ISIqNihRJnN0ZXA9NiIiI2tRI3Q9RiQjIiNLIiNEUSpBQlNlcnJvcj1GJCQiJyJ6RiIhIio=NihRJnN0ZXA9NiIiI2xRI3Q9RiQjIiM4IiM1USpBQlNlcnJvcj1GJCQiJytFOCEiKg==NihRJnN0ZXA9NiIiI21RI3Q9RiQjIiNMIiNEUSpBQlNlcnJvcj1GJCQiJ2J2OCEiKg==NihRJnN0ZXA9NiIiI25RI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInZ0U5ISIqNihRJnN0ZXA9NiIiI29RI3Q9RiQjIiNNIiNEUSpBQlNlcnJvcj1GJCQiJz56OSEiKg==NihRJnN0ZXA9NiIiI3BRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInTkw6ISIqNihRJnN0ZXA9NiIiI3FRI3Q9RiQjIiIoIiImUSpBQlNlcnJvcj1GJCQiJzkqZSIhIio=NihRJnN0ZXA9NiIiI3JRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInZVk7ISIqNihRJnN0ZXA9NiIiI3NRI3Q9RiQjIiNPIiNEUSpBQlNlcnJvcj1GJCQiJ3QwPCEiKg==NihRJnN0ZXA9NiIiI3RRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInbG08ISIqNihRJnN0ZXA9NiIiI3VRI3Q9RiQjIiNQIiNEUSpBQlNlcnJvcj1GJCQiJ1BIPSEiKg==NihRJnN0ZXA9NiIiI3ZRI3Q9RiQjIiIkIiIjUSpBQlNlcnJvcj1GJCQiJyZSKj0hIio=NihRJnN0ZXA9NiIiI3dRI3Q9RiQjIiNRIiNEUSpBQlNlcnJvcj1GJCQiJ1VnPiEiKg==NihRJnN0ZXA9NiIiI3hRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCInJSlHPyEiKg==NihRJnN0ZXA9NiIiI3lRI3Q9RiQjIiNSIiNEUSpBQlNlcnJvcj1GJCQiJ0MqNCMhIio=NihRJnN0ZXA9NiIiI3pRI3Q9RiQjRiUiI11RKkFCU2Vycm9yPUYkJCIndHJAISIqNihRJnN0ZXA9NiIiIyEpUSN0PUYkIyIiKSIiJlEqQUJTZXJyb3I9RiQkIidKWUEhIio=NihRJnN0ZXA9NiIiIyIpUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJzBCQiEiKg==NihRJnN0ZXA9NiIiIyMpUSN0PUYkIyIjVCIjRFEqQUJTZXJyb3I9RiQkIictLUMhIio=NihRJnN0ZXA9NiIiIyQpUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJ0UkWyMhIio=NihRJnN0ZXA9NiIiIyUpUSN0PUYkIyIjVSIjRFEqQUJTZXJyb3I9RiQkIicmb2MjISIqNihRJnN0ZXA9NiIiIyYpUSN0PUYkIyIjPCIjNVEqQUJTZXJyb3I9RiQkIickR2wjISIqNihRJnN0ZXA9NiIiIycpUSN0PUYkIyIjViIjRFEqQUJTZXJyb3I9RiQkIidHVEYhIio=NihRJnN0ZXA9NiIiIygpUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJ0VLRyEiKg==NihRJnN0ZXA9NiIiIykpUSN0PUYkIyIjVyIjRFEqQUJTZXJyb3I9RiQkIiciZSNIISIqNihRJnN0ZXA9NiIiIyopUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJzBBSSEiKg==NihRJnN0ZXA9NiIiIyEqUSN0PUYkIyIiKiIiJlEqQUJTZXJyb3I9RiQkIicrQEohIio=NihRJnN0ZXA9NiIiIyIqUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJ3dBSyEiKg==NihRJnN0ZXA9NiIiIyMqUSN0PUYkIyIjWSIjRFEqQUJTZXJyb3I9RiQkIidSRkwhIio=NihRJnN0ZXA9NiIiIyQqUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJylcViQhIio=NihRJnN0ZXA9NiIiIyUqUSN0PUYkIyIjWiIjRFEqQUJTZXJyb3I9RiQkIidmWE4hIio=NihRJnN0ZXA9NiIiIyYqUSN0PUYkIyIjPiIjNVEqQUJTZXJyb3I9RiQkIidJZk8hIio=NihRJnN0ZXA9NiIiIycqUSN0PUYkIyIjWyIjRFEqQUJTZXJyb3I9RiQkIic+d1AhIio=NihRJnN0ZXA9NiIiIygqUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJ1AnKlEhIio=NihRJnN0ZXA9NiIiIykqUSN0PUYkIyIjXCIjRFEqQUJTZXJyb3I9RiQkIicoKT5TISIqNihRJnN0ZXA9NiIiIyoqUSN0PUYkI0YlIiNdUSpBQlNlcnJvcj1GJCQiJyNvOSUhIio=NihRJnN0ZXA9NiIiJCsiUSN0PUYkIiIjUSpBQlNlcnJvcj1GJCQiJ0p4VSEiKg==

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