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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1
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0answers
180 views

Solving a Volterra integral equation

I review this question Solving a Volterra integral equation numerically. But I can not understand that. I have the following code: ...
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0answers
45 views

NIntegrate::inumr Error For Multiple NIntegrate Operations

I would like some help trying to use Mathematica (I just started using it!) to compute the numerical integration of a complicated function (assigned "longitudinalWake" in this example). Essentially, I ...
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1answer
121 views

Nested Integrals Using NIntegrate Not Converging

I have a mathematica script/code that I wrote that involves a few nested NIntegrate functions but its not converging. I let it run for about a week before calling it quits. I am a beginner with ...
5
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2answers
2k views

Numerically solve an integro-differential equation

So the problem is to numerically solve this Integro-Differential Equation, $$-v \frac{\:\mathrm{d}\kern0.1mm x(\zeta)}{\:\mathrm{d}\kern0.1mm \zeta} + \psi(\zeta) x(\zeta) + \int_{0}^{\zeta} f(\zeta, \...
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1answer
181 views

Numerical solution to an integral equation

I know this question mayn't be new, but here is my problem: I have to solve this integral equation (numerically, of course, except from very few special cases): $$\phi_{\nu}(t) = 1 - q\int_0^t \frac{...
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1answer
198 views

How to solve the integro differential equations with matrix

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 $\operatorname{diag}$...
3
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1answer
271 views

exponential differential integral equation

I have a following equation, which has a singular kernel, ...
2
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1answer
153 views

NDSolve cannot solve an ODE system with functions given as integrals-

The problem is that my Mathematica programme cannot solve the differential algebraic equations system. To simplify the problem as much as possible I will consider only the differential equation (which ...
2
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2answers
140 views

Unable to integrate function using Integrate

I'm looking to the result of the following integral: $$\int_0^{\infty} f(g)\exp(-tg) dg $$ where: $f(g) = \frac{ckg^{(c-1)}}{(1+g^c)^{k+1}}$ is a PDF not defined in 0 but with $\int_0^\infty f_G(g) = ...
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1answer
228 views

How to validate the solution of a system of integro-differential equations?

I have successfully solved a system of integro-differential equations. The system is ...
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1answer
90 views

Stop iteration during solving of an Integral equation

I am trying to solve the following integral equation numerically in mathematica: $f(x) = 1 + \int_0^1 dy \left(1-3xy\right)f(y)$. The exact solution is $f(x)=\frac{8}{3}-2x$. I can get the desired ...
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1answer
402 views

Recursive Function Numerical Integration

I just tried to modify a code snippet for Neumann series to the Fredholm integral equation $ f(x)= \sqrt{x} - \int^1_0 dy\; f(y) \sqrt{x y} $ which I read in another post: How to solve an integral ...
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0answers
262 views

Solving Integral equation by iteration

I am trying to solve coupled integral equation by iteration following the procedure that has been discussed in http://www.mathematica-journal.com/issue/v9i2/contents/IntegralEquations/...
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1answer
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 ...
5
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2answers
435 views

NIntegrate into NDSolve with variable integrand

I need to solve an integral into an ordinary differential equation like this: NDSolve[{y'[x] == x + NIntegrate[y[r], {r, 1,x}], y[0] == 1}, y, {x, 0, 1}] Note ...
2
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1answer
228 views

Numerical solution of singular non-linear integral equation

I want to extend this collocation method based mathematica scheme to solve following non-linear integral equation (Cauchy/Carleman type): $$B(v)/(1-v) \int_{0}^{1} \mathrm{d}x B(x) (1-x)/(v-x) = 1 $$ ...
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1answer
212 views

How to solve and plot Definite Integral with Symbolic Limits

I need to plot g1, g2, g3 and g4 expressions. To do that, I am trying to evaluate the double defined integral in the three expressions, however I am having issues because one of the integration limits ...
3
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1answer
839 views

Solve integro differential equation numerically [duplicate]

I want to solve the following equation numerically: with initial condition y[0]=0 and y'[0]=0 I tried to do so by using the NDSolve function: ...
8
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3answers
198 views

Numerically solving an ODE whose right-hand side involves an integral

In a 1955 paper on surfaces of constant negative Gaussian curvature, Marc-Henri Amsler defines a function $w(x)$ by giving the ordinary differential equation $$w'(x)=\frac{1}{x}\int_0^x \sin(w(t))dt,$$...
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1answer
232 views

Why doesn´t Mathematica solve the integral Integrate[Sqrt[a^2*(Sin[x])^2+1],{x,0,2*Pi}]?

I have to solve that integral and I am sure it is good written. It is an elliptical integral but Mathematica just doesn´t solve it. What is the result to that integral? ...
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0answers
248 views

How to use Halton sequence in Quasi Monte-Carlo integtation

I am trying to use Halton sequence numbers for MC estimator for rendering equation. At the moment I pass one instance of .Net Random object and get next number every time using same object thought the ...
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0answers
62 views

2-dimensional formatting for integration

So I am trying to integrate the function x^2 * Sin^2[n Pi x / a], {x,0,a}. The code I am using is in the "two-dimensional formatting" of mathematica: I am using Esc ...
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1answer
174 views

nonlinear integral equation

I have a non-linear integral equation that I'd like to solve with Mathematica: g[y_] := y^2; h[y_] := y^2/2 + c; func=(g[y] f[y]/Sqrt[h[y]^2 + f[y]^2]);
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0answers
160 views

Numerical solution of integral equation [closed]

I am trying to solve this integral equation numerically: $$f(x)=\int_a^b \frac{g(x)\,f(x)}{\sqrt{h(x)^2+f(x)^2}}\, dx$$ where $g(x)$ and $h(x)$ are known functions, and the limits of integration ...
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1answer
198 views

How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...
3
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1answer
126 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
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1answer
187 views

Solve for Joint Distribution Function

I wish to find a joint PDF $h(p,b) $or CDF $H(p,b)$, given the following expression: $(1-L) r \int _0^r\int _0^{\frac{p}{1-L}}h(p,b)dbdp- r L \int _0^r\int _0^{\frac{p-r}{1-L}+\frac{r}{L}}h(p,b)dbdp=...
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1answer
831 views

How to solve a system of integral equations [closed]

I am trying to solve a system of equations as follows... f1[t]/3 == (1/3)[Integrate[f3[t], t]] f1[t]/(6/5) == Integrate[f2[t], t] f3[t] == Integrate[f1[t], t] I ...
2
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2answers
150 views

Integral equation solving

So there is this equation that I have to numerically solve for T: Q/(3nRT) = f(T/300) - f(T/77) Here Q = 920.364, n = 0.24, R = 8.314 while f is defined as the ...
0
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1answer
292 views

How do I solve a nonlinear Fredholm integral equation?

$u(x)= 1/3+\int_{0}^{1}x\,t\sqrt{u(t)}\,dt$ u[x] == 1/3 + Integrate[x t Sqrt[u[t]], {t, 0, 1}] Any ideas on how to treat such a problem with Mathematica ...
5
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1answer
546 views

Solving PDE involving Hilbert transform numerically

I'm trying to solve the following equation numerically: $$u_{tt}-\mathcal{H}(u_x)=A^2_{xx},$$ where $\mathcal{H}$ is the Hilbert transform and $A$ is a prescribed forcing function which we assume ...
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0answers
290 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
3
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2answers
122 views

Solving an integral equation for upper boundary

I am reading a paper on High Harmonics Generation (HHG) and a Lewenstein model The paper is here. I would like to reproduce some results but I am stuck at the following problem. I have: $$p(\tau_b,\...
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0answers
104 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
1
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1answer
419 views

Solve a function to find the optimum value of parameter in mathematica [duplicate]

I have a complicated function as shown It doesn't have a standard integration as far as I know. Now, numerical integration of the left hand side function over a set of points gives the right hand ...
2
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0answers
69 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...
2
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0answers
382 views

Numerical solution to integral equation

I have an integral equation where one factor $f(t)$ in the integrand is defined in terms of an integral equation where it is again a factor. $\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + h[t]$...
9
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3answers
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: ...
2
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1answer
289 views

Integral equation

I'm trying to solve the following integral equation: Integrate[-k/2 Exp[-k Abs[x-z]] f[x], {x,0,d}] == a f[z] Differentiating twice with respect to z should ...
1
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1answer
293 views

RSolve with integrations

I want to solve this question with Mathematica. $$T_0(t)=c(t),\quad T_n(t)=a\int_0^t T_{n-1}(s)\, \mathrm{d}s+b(t).$$ Is it possible to solve $T_n(t)$ with RSolve?...
5
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1answer
525 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
1
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1answer
252 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at solving ...
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1answer
1k views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
7
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1answer
1k views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by <...
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1answer
310 views

Complex Integration

There are some sequential functions: ...
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1answer
151 views

Mathematica can't solve simple force-generated-by-cuboidal-planet integral?

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6
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1answer
647 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
0
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2answers
115 views

Simplify integration result with conditions

Let's say I have integral Integrate[1/(1 + (f^2/B^2)), {f, 0, Infinity}] The result is $$\text{ConditionalExpression}\left[\frac{\pi }{2 \sqrt{\frac{1}{B^2}}},\...
5
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1answer
1k views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
1
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2answers
311 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...