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

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0
votes
1answer
555 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
693 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
2k 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
551 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
882 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. ...
7
votes
1answer
507 views

Using physical dimensions in Mathematica DSolve

I would like to calculate a system of two differential equations in Mathematica using DSolve, like: ...
7
votes
2answers
1k 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
967 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
719 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
666 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
1k 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 ...
25
votes
4answers
1k 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 ...
14
votes
1answer
577 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 ...