# Questions tagged [integral-equations]

Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

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### Solving a Volterra integral equation numerically

I would like to solve for $P(t)$, in Mathematica, a Volterra integral equation of the 2nd kind. It is: $$P(t) = R_0(t) + \int_0^t P(t') R_0(t-t')dt'$$ I know the function $R_0$ and would ...
4k views

### How to plot and solve the numerical solution of a integro-differential equation

I have a integro-differential equation of the form $y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$ My code is: ...
2k views

### How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
602 views

### Solving an integro-differential equation with Mathematica

I try to solve a nonlinear integro-differential equation with this code. Here i used a periodic condition. ...
14k views

### Integral equation numerical solution with NDSolve

I'm trying to solve something like: f[x] == Integrate[f[x]*g[x]] where g[x] is known and f[x]...
6k views

### How to solve a non-linear integral equation?

I have a non-linear integral equation that I'd like to solve with Mathematica: $$\int_{0}^{1} \mathrm{d}x \frac{B(x) v}{(B(x) + B(v))^2} = 1$$ ...
293 views

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### Solving Integro-differential equation numerically with shooting method

This question is related a question I previously asked here Solving integro-differential equation with boundary condition at infinity and for which a solution was found . Now I am dealing with a ...
245 views

### How to speed up the integral in NDSolve?

On the MMA.SE, there have been several question on how to solve equations including integral using NDSolve, see example 1, example 2, and example 3. Many people, ...
245 views

### Solving integro-differential equation with DSolve in MMA 11.0

In this question DSolve(symbolic solution) gives wrong answer. I analyzed the 13 equations in which DSolve gives the same ...
539 views

### how can I solve integrals including recursion of some sequences of functions

I would like to solve the equations as given below in mathematica. I have written some codes before but I have no idea when there is sub indexing to indicate the series of functions. I will be very ...
546 views

### NDSolve: Couple PDE and ODE involving integral

I am trying to numerically solve an equation with NDSolve, where there is a ODE coupled to a PDE, like the following: ...
688 views

### Testing the convergence when solving an integral equation

I am trying to find the solution of an integral equation such that a certain convergence criterion is fulfilled. Now the problem is that the function doesn't look like what I am actually expecting, ...
60 views

### Solve integral equation by iteration

For[{n = 1, y[x_] = 1}, n < 4, n++, y[n][x_] = 1 + Integrate[y[n - 1][t]^2 + t^2, {t, 0, x}]; Print[{n, y[n][t]}]] here how can I get table of values ...
181 views

### How to solve this differential equation analytically?

How can I DSolve the following differential equation? Is there an analytical answer to this equation? ...
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### How to Integrate the Derivative of a function with Assumptions on the function?

I have a monotonic increasing function g and constant αsuch that ...
189 views

How I can obtain the $n^{th}$ approximation of the following Operator form integral equation? $F(t)=A(t)+\int_0^tds B(s)F(s)$, where $A(t)=\bigg{(}\begin{matrix}t&0\\Cos(t)&1 \end{matrix}\... 1answer 327 views ### iteratively solve integral equation Updated: I am solving the following integral equation for$f(k)$$$f(k)=-\iint d^2p\,d^2q\frac1{g(p)}\frac1{g(p-q)}\left(\frac 1{g(k-q)}-\frac1{g(-q)}\right)$$ where$g(k)=k^2+f(k)$so the ... 1answer 4k views ### integration on real domain only! i am trying to integrate a real valued function. For some reason, Mathematica gives an answer in the complex domain. I'd be grateful for your answers. Here is the integral: ... 1answer 108 views ### Solving IDE system using FDM based on NDSolve`FiniteDifferenceDerivative I wanted to solve the following system of integro-differential equations (IDEs) using finite difference method (FDM).$y_1''(t)+t^2y_1(t)-y_2''(t)+\int\limits_0^t[(t-x)y_1(x)+y_2(x)]\mathrm{d}x=(2+t^...
I have integro-differential equations like $X'(t)=\operatorname{diag}(\int_0^t X(t) dt)AX(t)-X(t)$, where $A$ is a known $N\times N$ matrix and $X$ is a $N\times 1$ vector, and $\operatorname{diag}$...