# Tagged Questions

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

283 views

### How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
236 views

### Coupled Nonlinear Differential Equations Problem

I have a big problem solving a set of coupled nonlinear differential equations using NDSolve. Solving the equations by themselves works quite well but if I want ...
293 views

### Second order differential equation

Hey guys I need someone to give me a hand on this. I don't know if this is too complicated or it's just the lack of knowledge I have on Mathematica. I'm trying to solve the following equation but ...
412 views

I was trying to solve the initial value problem $$u'(t) = \sqrt{u(t)} + \frac{1}{n+1}, \, u(0) = 0$$ using DSolve: ...
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### Solving with DSolve recursively

I need to find $f(x,n)$ in the interval [0,1] defined by recursion, $$\frac{d f(x,n+1)}{dx} = f(x,n)$$ with boundary conditions $f(0,n+1) = 1$ and $f(x,0)=1+ x$ Using ...
226 views

### Solution of differential equation in terms of incomplete gamma function

I need help in solving equation 15 and 16 either manually or in Mathematica to get the solution in terms of the incomplete gamma function. This is what Mathematica tells me. I can't understand ...
230 views

### How to use initial fixed timestep, then decrease it according to dependent variable, while spatial stepsize is fixed

I am trying to solve an advection equation. I want to force constant spatial step size (x dimension) with the “MethodOfLines” option, whereas I want to use initially fixed time step size 0.01 then ...
130 views

### Why I can not get the plot when I use NDSolveProcessSolutions?

Why I can not get the plot when I use NDSolveProcessSolutions? Anyone can give me a clue. Thanks a lot! ...
218 views

### Trouble to assign solution of differential equation to a function

I have written a function to Solve the following differential equation where the number n (called in my code Nphoton) is a variable. Nevertheless I have troubles to assign the solutions ...
70 views

### DSolve results not what expected

I have the following formula: s'[t] == 230.94 Tan[0.914743 - 0.138564 t] When I solve this by hand I get: ...
3k views

### Solve Laplace equation using NDSolve

I am new to Mathematica, a friend recommended this software and started using it, in fact download the trial version to know. I recently did a program in C to calculate numerically the solution to ...
590 views

### Save output of NDSolve to a file

I am solving following differential equation using Mathematica, ...
190 views

### Simpler code evaluating Dickman's function?

I've read here that Mathematica 10 can Obtain symbolic solutions to delay differential equations. Would that help in numericaly evaluating Dickman's function $\rho(u)$ ? It is a delay differential ...
287 views

### reconstruct a 3D curve from discrete curvature and torsion

I tried to reconstruct a 3D curve with given curvature and torsion. I saw some threads talking about using runge kutta. However, as far as I see that they required curvature and torsion were ...
2k views

### Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
202 views

### How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In ...
227 views

### Differential Equations: Solving a second order ODE with DSolve

I have the following equation h''[η] + (2 a'/a) h'[η] + (k)^2 h[η] == 0 2 a'/a = 1.3551 with boundary conditions ...
137 views

### DSolve not returning “trivial” solutions [duplicate]

When I enter this DSolve[y'[x]^2 + y[x]^2 == 1, y[x], x] the answer I get is ...
254 views

### NDSolve fails for certain choices of parameters and solve range

I'm trying to solve a pair of coupled ODEs with NDSolve. I know roughly what the solution should look like (both should give periodic functions, pi/2 out of phase, the amplitude of which damp towards ...
243 views

### Numerically solving systems of (first order) linear delay differential equations

I was wondering, how to solve such a system with mathematica? I found the NDsolve function, but in the reference is not mentioned if it is possible to solve a system of equations.
162 views

### NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
300 views

### Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
144 views

### Error when extending 1-dimensional PDE to 2 dimensions

I want to calculate how magnetic flux is trapped in a superconductor near the interface superconductor/vacuum. This problem already was solved analytically by J. Pearl for cylindrical symmetry (if ...
238 views

### Extract data from NDSolveValue result

Okay this is a very newbie question. I have coded a sample problem that solves the heat diffusion equation on an annulus. Here's what I have: ...
1k views

### Driven simple harmonic oscillator — amplitude of steady state motion

I am (partly as an exercise to understand Mathematica) trying to model the response of a damped simple harmonic oscillator to a sinusoidal driving force. I can solve the differential equation with ...
871 views

### PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
403 views

### Real and Imaginary parts of solutions to a complex linear ODE system

Consider a complex linear ODE system $x'=Ax$, where $$A=\left( \begin{matrix} 0&1\\ -2&-i \end{matrix}\right).$$ One can first find the eigenvalues and eigenvectors using ...
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### Error when using EquationTrekker

I just got to know EquationTrakker because I need to do phase graphs for my classes. When I load it ...
174 views

### NDSolve solution violates initial conditions

I have the following code: ...
290 views

### Two problems with NDSolve when using Method -> Projection

I tried to solve a system first order differential equations together with a constraint equation. I use the Method -> Projection to check if the constraint holds ...
2k views

### DSolve not finding solution I expected

Try to solve the following ODE via DSolve \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. The ...
399 views

### How can I apply calculus to functions obtained from NDSolve?

Originally, I asked the question below, but the real underlying issue is as follows: When we solve an ODE numerically, I get the answer like this: ...
100 views

### How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
I am manipulating partial differential equations symbolically, and would like to get the easily readable form $\rho \frac{\partial v}{\partial t}$, leaving variables implicit. Based on suggestions ...