# Tag Info

Accepted

### Symbolic solution(s) to generalized Heat equation

A first step would be to implement a convenience function that can automatically apply the method of separation of variables to separable types of equations. To show that the steps could in principle ...
• 95.2k

### Nonlinear differential equation: numerical solution

Introduction I think there are several questions on this site about ODEs of the form $$(x-a)^2 u''(x) = F(x,u,u')$$ with an initial condition at $x=a$. There is no general guarantee that solutions ...
• 216k
Accepted

### Numerically solve the initial value problem for the 1-D wave equation

I've waited for this question for a long time :) Fully NDSolve-based Numerical Solution There actually exist 2 issues here: NDSolve can't handle unsmooth i.c. ...
• 52.5k

### Symbolic solution(s) to generalized Heat equation

Here is extensions to @Jens answer (I think) also relying on possible separation of variable. It is not meant as an independent answer, but complements it. First extend his answer to 2D ...
• 21.7k

### How to solve ODE with boundary at infinity

The finite element method can be used on this problem if we make a change of variables to convert the domain $[0, \infty)$ to a finite interval. I believe only ...
• 216k
Accepted

### How to solve ODE with boundary at infinity

You can use ParametricNDSolve to implement a shooting method. Define a finite version of "infinity". inf = 5; Define the ...
• 4,799

• 13.6k
Accepted

### Frequency domain Maxwell equations with PML boundary conditions

I'm not that familiar with electromagnetism, either, but I think there're at least 4 issues in your solving process: There's no need to "consider only the magnetic field", because electric field is ...
• 52.5k
Accepted

### Boundary Condition for Schrödinger Equation in Infinite Range

Since OP has found this interesting post, let me try to implement the exterior complex scaling method mentioned there. First, make the transform \$x= \left\{\begin{array}{cc} & \begin{array}{cc}...
• 52.5k
Accepted

### Error when solving 't Hooft-Polyakov radial equations using NDSolve

Once again, compared to "Shooting" method that is the default and currently the only available method for solving nonlinear boundary value problem (BVP) ...
• 52.5k

### An ODE system easily polluted with spurious eigenvalues

NDEigenValues handles the pair of first-order equations in the question much more accurately, when it is converted into a single second-order equation. ...
• 58.4k
Accepted

### An ODE system easily polluted with spurious eigenvalues

The additional problem added to the end of the question can be solved in a similar manner. Begin with ...
• 58.4k
Accepted

### Where is the numerical solving breaking down?

For this problem, you must specify a solution method. Since the system of equations is nonlinear and the equation for y does not contain derivatives with respect to ...
• 34.1k

### Where is the numerical solving breaking down?

Fully NDSolve-based Solution Adjustion for spatial step size together with temporal step size helps. I've used parameters mentioned in the comment for testing: <...
• 52.5k
Accepted

### Numerical solutions of active 1D wave equations

NDSolve-based Solution ...
• 52.5k

### Nonlinear differential equation: numerical solution

This question seeks the separatrix of a nonlinear ODE over the range {0, Infinity}. As noted by Michael E2, many such problems have been presented on this site. (...
• 58.4k
Accepted

### Using DSolve with a boundary condition at -Infinity

This is the solution of your equation without the boundary conditions: ...
• 35.1k
Accepted

### Numerical solution of nonlinear boundary value problem

This system of second-order nonlinear ODEs, like many others in this site, is difficult to solve numerically, because the desired asymptotic solution is a separatrix. As a consequence, infinitesimal ...
• 58.4k