How to add "erf()" part to the ode solution?

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Ali Deniz 2022-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/1830873-how-to-add-erf-part-to-the-ode-solution

评论： Ali Deniz 2022-10-20

采纳的回答： Torsten

Hi,

I have the ODE : y' = -x+2+10*e^(10*(x-1)^2)

I have numeric solution of below:

I have a analytical solution of ODE below:

y (x)= C1 + 2*x - x^2/2 + (10^(1/2)*pi^(1/2)*erfi(10^(1/2)*(x - 1)))/2, y(0)=1

when I plot the analytical solution without "erfi()" part, the graph is below:

The curve is similar to numarical solution but there is evident error. I think, this error is because of "erf" part of the analytical solution. How can I plot the analytical solution with the "erf()" part. Thank you.

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采纳的回答

Torsten 2022-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/1830873-how-to-add-erf-part-to-the-ode-solution#answer_1079143

编辑：Torsten 2022-10-19

在 MATLAB Online 中打开

syms x y(x)

eqn = diff(y,x) - (-x+2+10*exp(-10*(x-1)^2)) == 0;

cond = y(0)==1;

sol = dsolve(eqn,cond)

sol =

fplot(sol,[0 6])

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Les Beckham 2022-10-19

在 MATLAB Online 中打开

Without the symbolic toolbox:

x = linspace(0, 6, 1000);

rt = sqrt(10);

rp = sqrt(pi);

y = 2*x - x.^2/2 + (rt*rp*erf(rt))/2 + (rt*rp*erf(rt*(x-1)))/2 + 1;

plot(x,y)

grid on

Ali Deniz 2022-10-20

Thank you very much.

-Ali

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