Linked Questions
17 questions linked to/from Unexpected result of summation
2
votes
1
answer
299
views
Computing the coefficients for Gaussian integral [duplicate]
I wrote a small script to find the Gaussian integral points and weights:
...
- 2,591
10
votes
2
answers
1k
views
Fredholm Integral Equation of the 2nd Kind with a Singular Difference Kernel
After reviewing the literature, I could not find an analytic solution to the equation
$$\int^{1}_{0}dx\frac{f(x)}{|x-y|^{2/3}}=cf(y)$$
for $f(y)$, where $c$ is a constant and $y\in[0,1]$.
I'm ...
- 347
6
votes
3
answers
1k
views
Why Gauss-Legendre Quadrature should keep the number of integral points less than about 50?
I wanted to use Gauss-Legendre Quadrature to calculate an integral as follows：
When n=10 and some other number(except odd numbers),the numerical result is the same as theoretical result.
...
- 93
9
votes
1
answer
1k
views
Two-dimensional catenary in Mathematica
I'm working in Mathematica to plot a 2-d catenary in Euclidean space according to this Math Stack Exchange Link, specified with a square Dirichlet boundary condition.
Here's what I've coded using ...
- 93
2
votes
2
answers
971
views
Why Gauss-Legendre rule gives wrong result for piecewise polynomial function?
I implemented the Gauss-Legendre rule as follows:
$$\int_0^1f(x)dx=\frac 1 2 \int_{-1}^1f(\frac{1+x}{2})dx=\sum_{i=0}^{4}A_if(\frac{1+x_i}{2})$$
...
- 655
9
votes
2
answers
597
views
Is it possible to take a numerical (integral) average of the dependent variable, within NDSolve, at each iteration?
tl;dr: want to integrate (average) the dependent variable within NDSolve.
I am currently trying to implement a basic diffusion-advection equation for a reactant, A. The species is converted between A ...
- 93
6
votes
2
answers
350
views
How do I improve the style, efficiency, and versatility of this code?
I have a math problem that I have solved analytically. I now want to generate a number of graphs based on different parameter values. My problem is threefold:
It takes a couple of minutes to produce ...
- 61
8
votes
1
answer
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 <...
- 1,257
3
votes
1
answer
1k
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:
...
- 51
3
votes
2
answers
427
views
Need help to speed up the Gaussian quadrature
I am trying to compute the $L_2$-norm of the solution $y(z,t)$ of a PDE with Gauss quadrature using the following code, where $z$ is space position and $t$ is time, then to construct it as a function ...
- 823
2
votes
1
answer
1k
views
gaussian integration
I'm new on Mathematica and I am an engeneer with only a little base of numerical computation. I have to integrate a trigonometrical function numerically with a Gauss integration. The function is:
<...
- 65
1
vote
1
answer
969
views
NonlinearModelFit runs too slow when fitting data to a function that does multiple numerical integrations
I have a function of several parameters defined in a module which does multiple numerical integrations. Then I try to fit that function to some sample data via with ...
- 11
0
votes
2
answers
442
views
4
votes
1
answer
252
views
A Trial Boundary Element Approach to Solving Integral Equation
I am trying to numerically solve an integral equation in Starfield and Crouch textbook (Boundary Element Methods in Solid Mechanics: With Applications in Rock Mechanics and Geological Engineering), ...
- 423
3
votes
1
answer
371
views
How to handle this constant-interval integral in ODE?
The problem is to solve a system of nonlinear equations with a definite integral. $Q_i(x), i=1,2,3, x \in [-\text{max},\text{max}]$
\begin{align*} a_iQ_i''(x)-b_i(\vec{Q})-d_i\int_{-\text{max}}^{\text{...
- 4,758
1
vote
1
answer
131
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 ...
- 21
0
votes
0
answers
143
views
Need help to replace Nintegrate with Simpson's Rule
I have a mathematica code for solving numerical inverse Laplace transform (Credit to Mr. Patrick O. Kano), but sadly the code is using Nintegrate, and i want to use ...
- 373