Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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9
votes
1answer
590 views

How to tell mathematica not to resolve stiffness issues

Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
4
votes
2answers
2k views

Problem with the DSolve function

OK guys, here's the thing, Mathematica does not return a solution for this system of differential equations: ...
2
votes
1answer
309 views

Laplacian or Grad of an InterpolatingFunction

For obtaining a Schlieren image from an equation for density, I need to calculate the first derivative of density and make a contour plot. The below code snippet calculates the first derivative w.r.t ...
2
votes
2answers
444 views

How to solve a Differential Equation with DSolve with Function Coefficient?

Suppose I have v[x_] = (1.453 Sech[x + 1])^2 + I Sech[x + 1] Tanh[x + 1] And I have to solve the equation: ...
2
votes
2answers
708 views

optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
2
votes
1answer
497 views

Optimizing a function involving NDSolve results in error messages

I want to minimize a function f with NMinimize but an error occurs that says: ...
9
votes
1answer
299 views

How can I eliminate a function in a system of PDEs, Maple-style?

Maple can separate and eliminate a function in a system of PDE equations, with casesplit in the PDEtools package. How to do ...
3
votes
2answers
531 views

Eliminate doesn't work in Mathematica

Hello Mathematica users, I have problems trying to eliminate variable $Q(x,y)$ froma PDE, but Mathematica output is just True. The problem is that I already found ...
2
votes
1answer
381 views

Inconsistent initial and boundary conditions

I have a 4th order nonlinear PDE with the following BCs and IC: ...
4
votes
1answer
726 views

Incorrect solution of diffusion equation with Neumann boundary conditions

I want to set up a PDE model, which takes a two-dimensional diffusion equation into account. The key problem is that I have some trouble in solving the two-dimensional diffusion equation numerically. ...
0
votes
2answers
320 views

Plotting with NDSolve`StateData`

This question is a continuation of this. As answered by J.M., I am able to iterate a solution. However, I am unable to plot it. I am sure that this has to do with my inability to understand how the ...
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 ...
0
votes
2answers
284 views

NDSolve and results of the previous computations

I want to solve following system of ODEs: $ \Bigg\{ \begin{array}{} \frac{\partial C}{\partial t}=\frac{2W_b}{Rsin(\theta)}(1-\frac{C}{\gamma})+\frac{\nu}{\pi R^2}\frac{\partial C}{\partial Z} ...
0
votes
1answer
704 views

Plot is not showing [closed]

I've used Wolfram Mathematica 8 Trial version for two days. Any pointers are appreciated. Thanks in advance! EDIT: There are supposed to be 4 plots, but only 3 are showing. Everything works except ...
4
votes
2answers
657 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 ...
6
votes
2answers
368 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
10
votes
2answers
415 views

DSolve cannot solve for certain branches of the solution

Could somebody please tell me, why I am always getting an error message when trying to run the following code: ...
11
votes
2answers
899 views

How can I solve a difference-differential equation?

How do I ask Mathematica to try to solve a recursive relation that defines a sequence of functions? For example, suppose I know that $g_n(x) = g_{n-1}'(x)$ for $n > 0$ and that $g_0(x) = e^{2x}$. ...
3
votes
1answer
349 views

Solving an ODE numerically

I really appreciate it if anyone helps me with this: How can I solve this ODE and plot the answer for $x$ on $[0.6,5]$: $$ \begin{align*} -2xy'[x] = y''[x]+ 47.21 (-.0025 x^6 & + ...
5
votes
0answers
602 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 ...
1
vote
1answer
182 views

NIntegrate is resetting my variables and not giving me a result?

I am trying to check if mass conservation holds by integrating the area under a curve but to no avail. ...
6
votes
1answer
291 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
7
votes
1answer
303 views

Setting the DifferenceOrder Option

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
5
votes
1answer
1k views

NDSolve, Schrödinger equation, and decaying solution

I am trying to solve a Schrödinger equation for a particle hitting a step potential using NDSolve in Mathematica. Here is my code: ...
6
votes
2answers
609 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
19
votes
1answer
561 views

Publishing results obtained in Mathematica

I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer ...
11
votes
1answer
1k views

What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
11
votes
5answers
2k views

How can you compute Itō Integrals with Mathematica?

How can you compute Itō Integrals with Mathematica? I tried searching through the documentations but I didn't find anything. P.S. I was not at all sure how to tag this question. I had to put in at ...
0
votes
1answer
427 views

NDSolve does not give me the expected solution

I have an assignment where I need to compute chemical reactions by solving ODEs. I use NDSolve to do this. However, for one problem it does not give me the ...
3
votes
1answer
536 views

NDSolve Problem

I am trying to solve a chemical equilibrium ODE with NDSolve where one function is the argument to another. I.E. My equations look like: ...
4
votes
2answers
1k views

PDE Boundary Conditions

I am solving a PDE using Mathematica and I would like to know how to implement the condition that the two-variable function y[t,s] is zero whenever ...
6
votes
2answers
420 views

Very long Refine/Solve batch run - is my code broken, or just complicated?

So I'm trying to run some Mathematica code in batch mode from my university cluster. Specifically, I'm trying to find the equilibria of a system of ordinary differential equations. Inspired by the ...
7
votes
1answer
623 views

Extracting coefficients from a partial differential equation

Frequently, I come across the following problem: How to rewrite a complicated partial differential equation in a more clear way? I would like to create some order by collecting terms that are equal. ...
5
votes
1answer
353 views

Using physical dimensions in Mathematica DSolve

I would like to calculate a system of two differential equations in Mathematica using DSolve, like: ...
6
votes
2answers
702 views

Creating Plots for a Family of Solutions

I am wondering how do you set the parameters appropriately for $a_n,\,\alpha,\,\text{and }b_n$ to plot the family of solution of: $u_n(r,t) = [a_n\cos(k_n\alpha t)+b_n\sin(k_n\alpha t)]J_0(k_nr)$ ...
4
votes
1answer
702 views

Evaluation of a Variable Coefficient PDE

I am trying to render the solution of the following partial differential equation: $$ u = u(x,y)~;\quad \frac1{x^{2/3}}\partial_xu + x^3\partial_yu + \partial_y^2u + \partial_x^3u = 0 $$ ...
2
votes
2answers
469 views

Solution Curves and Order of Evaluation Question

I'm new to Mathematica, so I thought I'd try to exercise some solution curves. Consider a simple first order ODE: $y'(x)=\cos(x)$. We know the solution will be of the form $y = \sin(x)+c$ I ...
7
votes
2answers
444 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
4
votes
1answer
600 views

MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...
23
votes
4answers
805 views

How to use NDSolve to track equilibrium?

I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
13
votes
1answer
436 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...