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1
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0answers
67 views

Imaginary number appears in Integrate [on hold]

I had a problem in the following code because when I use Integrate, there will always be imaginary number in the result. I put my code here. The satisfactory result should look like eq 9.138, which I ...
3
votes
0answers
90 views

What can I do to improve the performance of my calculations?

I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed. I have an object whose unknown location is modeled ...
0
votes
0answers
29 views

Multivariable Delay Diff. Equ. with Ndsolve and Nintegrate

I'm trying to simulate the following equation in Mathematica for $u(x,t)$: $$\frac{1}{\alpha} \frac{\partial u(x,t)}{\partial t} = -u + \int_{-\infty}^\infty {\rm d} y w(y) f(u(x-y,t - |y|/v))$$ ...
1
vote
1answer
72 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
0
votes
0answers
50 views

Solving for a variable within a definite integral using FindRoot

I want to solve for P in this equation: Integrate[1/((P/(M*V)) - r*g - c*A*(V^2)*p/(2 M)), {V, 0, 26.82}] = s , where all constants are given except P. I've ...
3
votes
0answers
78 views

Non-linear integral equation

I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be ...
0
votes
0answers
53 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...
2
votes
1answer
91 views

Using Boole to integrate over region

I have a complex and long piecewise function to integrate, so I have written a Mathematica script that cuts the whole range of integration, evaluates the integrand in each region and then integrates ...
-3
votes
2answers
66 views

Find the value by using FindRoot command [closed]

The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the ...
0
votes
0answers
165 views

Solving a linear fourth-order fractional integro-differential equation

Definition: A real function $f(x)$, $x>0$ is said to be in space $C_\mu$, $\mu\in \Bbb R$ if there exists areal number $p$ ($>\mu$), such that $f(x)=x^pf_1(x)$, where $f_1(x)\in C[0,\infty]$, ...
6
votes
2answers
110 views

Integrate perfomance

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral in the new version of Mathematica. Here's the ...
-2
votes
1answer
191 views

Plotting a graph

Could anyone help me with plotting the following graph? Integrate (-Inf, Inf) (exp(-i*x*t))/((4*pi)((x-1)^2 +25)(exp(-100x) +1)) It's not a code obviously, but I ...
0
votes
1answer
549 views
0
votes
1answer
346 views
0
votes
0answers
127 views

System of integral equations with integrals on both sides

I'd like to solve the following equation numerically for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$: $\displaystyle\int_0^{\infty}\Big[L_1\Big(\frac{k^2}{2}\Big)\Big]^2e^{-k^2}L_m(k^2)\ dk=$ ...
2
votes
1answer
184 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 ...
2
votes
1answer
131 views

Integral of GeneratingFunction

I know that GeneratingFunction can be used to compute the generating function $\sum_{n=0}^\infty a_n x^n$ of a sequence $(a_n)_n$ via GeneratingFunction[a[n],n,x] ...
1
vote
1answer
412 views

Definite integral using Riemann sums [closed]

I just started learning Mathematica. It seems like a good program to learn. I only know some basics though. I came across this problem online which I want to learn how to solve: Write a ...
0
votes
1answer
82 views

Mathematical Theory - Integral [closed]

Consider this integral f[g_,b_]=NIntegrate[1/Sqrt[r+g+b],{r,0,Infinity}]; I have to get a value for b , and this value i get when f[g,b]==0 ( or the minimum ...
2
votes
1answer
326 views

Volterra integral equation : 'literally match the independent variables' message

I want to solve an Volterra type Integral equation, and as a practice I entered the following code to my mathematica: ...
0
votes
0answers
70 views

Some boundary issue of Integration

When I try to solve the integration f(x) as following (type it in the Mathematica) $ f(x)= \frac{1}{π} \int_{-1}^{1} \frac{\sqrt{1-y^2}}{(y-x)}dy $, I met some boundary problems. I have searched some ...
0
votes
0answers
103 views

Some questions about Integral Equation

I am trying to solve the finite Hilbert transformation like the following form $ f(x)= \frac{1}{π} \int_{-1}^{1} \frac{g(y)}{(y-x)}dy $ the given function f(x)=1 and I want to solve the g(x) I know ...
-1
votes
1answer
139 views

Newbie trying to calculate an integral for some second derivative - numerical value needed [closed]

I bought Mathematica (for Linux) today and am trying to calculate this integral: \begin{align} ...
0
votes
0answers
66 views

Evaluating multiple integral over a vector

I am trying to find an easy way to evaluate the following multiple integral from a question I asked on math.stackexchange. As you can see, the integral is over a vector of multiple variables. Is there ...
1
vote
0answers
69 views

Integrate boundaries defined as equations

Have you guys ever needed to define Integrate boundaries as equations? I tried to submit the equation as was written in original text but it seems that mathematica can't understand it. ...
1
vote
0answers
151 views
4
votes
1answer
355 views

Recursive Integration

I'd like to evaluate the following recursive integration using Mathematica $$ \ M(T) = \int_0^T\int_0^\infty e^{-\delta s}g(x,s)dxds\ +\int_0^T e^{-\delta s}f(s)M(T-s)ds\, $$ where $g(x,s)$ and ...
2
votes
2answers
161 views

Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$ d(a,b) = {(a+1)(b+1)(a+b+2) \over 2} $$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where $n \in ...
1
vote
0answers
276 views

Solving homogeneous Fredholm Equation of the second kind

I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e. $\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$ where $\lambda$ is the eigenvalue (to be ...
2
votes
2answers
97 views

How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?

Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below: ...
8
votes
1answer
950 views

solve an integral equation numerically

I am trying to find a numerical solution for an equation of the form: $$ f(t)=\int_{t_{min}}^{t} {\exp[2 (t^\prime - t)] E(t^\prime) f(t^\prime)} + \int_{t}^{0}{ \exp(t^\prime - t) E(t^\prime) ...
3
votes
2answers
409 views

Evaluating the integral of $\cos (\theta )\cos\left[\tan ^{-1}\left(\frac{a^2 \tan (\phi )}{b^2}\right)\right]$

I am trying to evalute the following integral: Integrate[Cos[θ] Cos[ArcTan[a^2/b^2 Tan[φ]]], {φ, 0, 2π}] I know that for $a=b$ I should get 0 out of the integral ...
1
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0answers
304 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, ...
0
votes
1answer
337 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: ...
9
votes
1answer
1k views

How to solve a non-linear integral equation?

I have a non-linear integral equation that I'd like to solve with Mathematica: Solve[Integrate[B[x] v / (B[x] + B[v])^2, {x, 0, 1}] == 1, B[v], {v}] This ...
0
votes
0answers
175 views

dealing with discontinuity at integration

My problem is about the solution of $2$ non-linear equations which have a single parameter. To be more precise, For given two densities; for example: ...
2
votes
1answer
130 views

Problem with numeric integration

I am having trouble with the UnitStep function as in the title. My problem is very simple, but I am not able to get a numerical result. I have ...
0
votes
1answer
113 views

Differential Equation help

I have a differential equation that looks like this: ...
0
votes
1answer
337 views

Solving an integral equation numerically for an unknown within the integral

I'm trying to solve an integral equation of the form Constant == Integrate [g(x)f(x,Efermi), {x,-200,200}], for the parameter ...
3
votes
2answers
3k 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 ...
1
vote
1answer
202 views

Need help evaluating definite integral to a function of Y

Suppose $Y = \sqrt{2T}\cos(U)$, $ 0 \le u \le \pi $, and $ 0 \le \cos^{-1}(\frac{y}{\sqrt {2t}}) \le \pi ) $, so $ -1 \le \frac{y}{\sqrt{2t}} \le 1 $, with all $ \mathbb{R}$. The iterated integral ...
7
votes
0answers
2k views

Integro-differential equation

I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation, $$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
0
votes
1answer
710 views

how to solve an implicit integral equation? (iterate to a functional fixed point?) [closed]

I reduced a (special case) of my problem to the following code. Even though in this special case all related functions are analytical, DSolve is not the tool for this, though I am indeed looking for a ...
12
votes
3answers
2k views

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 ...