19-Tanzanite

Solved

How to solve Integro-differential equation numerically?

Forum|Forum|1 year ago
June 5, 2024
2 replies
2043 views

Hi,

Is it possible to solve somehow with odesolve block integro-differential equation like below? Or how this type of eq can be solved numerically?

1_Untitled-11_MCP9.zip

Mathcad Usage

Best answer by Werner_E

I don't think that Prime would be able to solve that integral equation, but you can easily rewrite it (substitute y*=z') and then you could solve it symbolically

or that way:

A

AlfredFlaßhaar

15-Moonstone

After differentiation, a homogeneous linear second order differential equation with constant coefficients is obtained. The double zero of the characteristic polynomial is -1. Therefore, the solution has the structure y(t)=a*exp(-t)+b*t*exp(-t). The coefficients a and b are calculated from initial/boundary values.

C

Cornel

Author

19-Tanzanite

1_Untitled-11_MCP9.zip

A

AlfredFlaßhaar

15-Moonstone

Sorry, I have to correct myself, because the 5 was overlooked. The zeros of the characteristic polynomial are now lambda1=-1+2*i and lambda2=-1-2*i. Therefore y(t)=a*exp((-1+2*i)*t) +b*exp((-1-2*i)*t). Apply Euler's equation to this, according to which exp(i*y)=cos(y)+i*sin(y). Calculate the coefficients as usual from the initial values and after inserting them into the integral equation.

W

Werner_E

Answer

25-Diamond I

I don't think that Prime would be able to solve that integral equation, but you can easily rewrite it (substitute y*=z') and then you could solve it symbolically

or that way:

W

Werner_E

25-Diamond I

Additional remark:

If you want to solve an equation which is too complicated for Primes symbolic, you still can replace the integral by a function z(x) with z'(x)=y(x) and use a numeric solve block:

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