Questions on the use of numerical functions NIntegrate and NDSolve.
4
votes
1answer
161 views
NDSolve for a large system of simple ODEs
I am solving a system of many (more than 100) ODEs.
It is the kind of standard rate equation encountered in semiconductor physics.
Here is the system:
...
0
votes
1answer
66 views
Error messages when using NInverseFourierTransform
I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
7
votes
0answers
137 views
Numerically solve 2nd order differential equation with singularity
Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example:
$$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$
where ...
7
votes
0answers
1k 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|) ...
6
votes
0answers
64 views
Modify NDSolve`StateData (if possible)
I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData.
Now, the problem is, I'm not used to ...
6
votes
0answers
217 views
Optimizing NIntegrate for higher PrecisionGoal
By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
5
votes
0answers
169 views
4
votes
0answers
129 views
Artifacts in Line Plot from InterpolatingFunction
I have a periodic solution from an NDSolve that is producing an InterpolatingFunction. With the default plot settings, there is not enough PlotPoints/MaxRecursion to resolve the peaks in the function:
...
4
votes
0answers
399 views
Controlling the time step in NDSolve?
I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE.
I've also tried out ...
4
votes
0answers
222 views
Increase precision of custom function
I hope the title is not misleading:
Suppose I have a function that is quite complicated, e.g.
f[u_] := Exp[-Exp[- Abs[c.u]^a] Sin[d.u] Sin[(Abs[c.u]^a) ...
I ...
3
votes
0answers
66 views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
...
3
votes
0answers
226 views
Numerically solving PDE with high precision
I want to numerically solve the PDE
$\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$
with some initial and boundary conditions and given parameters $c$, $m$ and $l$.
Consider the code
...
3
votes
0answers
364 views
Solving a system of nonlinear equations self-consistently
I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
3
votes
0answers
410 views
How to Solve this ODE with Mixed Boundary condition
I have an ODE equation which is sort of
y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0
subject to the boundary conditions
...
2
votes
0answers
82 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
0answers
155 views
Is mathematica storing information it shouldn't store?
I'm seeking to find solutions to a numerical integration with a large set of parameter combinations (basically, I'm doing a brute parameter sampling). Yet, I believe the memory of the computer is ...
2
votes
0answers
139 views
FindRoot - Speed and errors
I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
votes
0answers
193 views
Inconsistent boundary and initial conditions: BC ignored altogether
Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary:
...
2
votes
0answers
163 views
Numerical-Symbolical Integration (Calculus)
I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals.
The problem with my function is ...
2
votes
0answers
125 views
EventLocator with LSODA?
Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
1
vote
0answers
82 views
Getting MemoryAllocationFailure from NIntegrate
When numerically calculating a double integral using NIntegrate over an infinite domain (with all options at their default), Mathematica 7 calculates my integral ...
1
vote
0answers
90 views
NDSolve diffusion equation over/underdetermined
I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak.
I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
1
vote
0answers
113 views
Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
1
vote
0answers
134 views
How can I speed up numerical integration of multidimensional integral?
I am numerically solving an integral equation that contains a double integral. I have managed to get a solution but it takes forever. I am wondering if there is a way to speed up numerical integration ...
1
vote
0answers
121 views
NDSolve equations contain solution from solving cubic equations
I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations.
In my problem, I first obtained 6 functions (ca1, ...
1
vote
0answers
296 views
Speed up Numerical Integration
EDIT:
I need to evaluate a very complicated multi-dimensional Integral. The dimension of the Integral depends on a variable j. Let's make my point clear with the ...
1
vote
0answers
165 views
fit using parametric equations
I have experimental data with two columns (x & y). I need to fit the data to two parametric equations of the form
$$y =\text{const}_1 \times
\left( \frac{\int _a^{b}\sqrt{\frac{\left( 1+\gamma ...
1
vote
0answers
118 views
Table not working with Plot
Because NIntegrate[] does not support parallel computation out of the box, I'm doing a simplified version by breaking the integration limit into pieces and using ...
1
vote
0answers
111 views
NDSolve Convergence test failure and significant effect of DifferenceOrder on eventual results
I am solving a non linear partial differential equation with what I call free boundary conditions (solid mechanicists would know this as simply supported).
I realized that this boundary condition ...
1
vote
0answers
131 views
Issue concerning stopping NDSolve through EventLocator
Greetings. As the question-title is written I am having some trouble with getting a numerical integration stopped at a certain event. This integration is done through the use of NDSolve and I have ...
1
vote
0answers
197 views
About doing an integral
For a given integer $N$ and some function $f(x,y)$ I want to be able to do an integration of the kind,
$\int_{0} ^{\infty} \prod_ {i=1}^N da_i e^{[\sum_{n=1}^{\infty} \frac{1}{n} \left[ N + ...
1
vote
0answers
195 views
1
vote
0answers
171 views
Integrating over a region without singularity gives an error indicating the function has singularity in that region
I have the following 2D region over which I want to integrate a function:
...
0
votes
0answers
83 views
NDSolve divergence in Mathematica 9
I have been working with Mathematica 7 and 8 to numerically solve partial differential equations by MethodOfLines of NDSolve. ...
0
votes
0answers
70 views
Which integration strategy to use for this product of polynomials?
What would be the ideal integration strategy for a function like this: $$f(x_1,x_2,\dots,x_N)=\prod_{i=1}^Nx_i^{c_i}\Theta(x_i-p_i)$$ where $x_i,p_i\in \mathbb{R}$, $\Theta$ is the Heaviside function ...
0
votes
0answers
69 views
FindFit and NIntegrate with dependency between integration variables
I am trying to use FindFit and NIntegrate in this situation:
...
0
votes
0answers
109 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:
...
0
votes
0answers
86 views
Issue with WorkingPrecision
I am having the following issue.
I am evaluating a numerical integral, and I need high precision to get good values of the function being integrated.
...
0
votes
0answers
127 views
Numerical solution of a system of ODEs
I have to solve set of coupled first order ODE's
$y_1=z$, $ y_2=\frac{dz}{dt} $;
$\frac{d^2y_1}{dt^2}=\frac{dy_2}{dt}=\frac{(p_s-p_f)}{p_s}g-\frac{9u}{2a^2p_s}y_2 $
Using the Euler method and the ...
