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

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19
votes
0answers
164 views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
3
votes
0answers
76 views

3D FEM with holes

I'm trying to create a finite element mesh with some spherical holes. To my mind the behavior is erratic but generally fails. I'm using MMA 10.0.2. In the following 3 different sets of holes are ...
0
votes
0answers
31 views

how to solve impulsive differential equation in mathematica [on hold]

this is my system, i need help to solve this.i want to know that how to put impulse condition in Solve command
0
votes
0answers
37 views

I need to solve the Mathieu equation: $y''(x)+(a−2q \cos(2x))y(x)=0$

I want to know what will be the boundary conditions? For integer order and $\pi$ periodicity? How I can find solution of equation?
0
votes
1answer
42 views

Assymptotically Solving ODE with free parameters

I have a first order ODE, $F(y[x], y'[x], A, B) = 0$. I want to solve this numerically (with the boundary value $y[1] = i$ ) but also with the following requirements: A and B are free parameters which ...
-3
votes
1answer
29 views

How do I solve and graph this coupled PDE?

How can I solve and graph v1 versus t and v2 versus t for a given x? Let A = 3, p = 2, B = 4. At t = 0, v1 = 2, v2 = 2. For the graph the range of t is [0,60].
0
votes
2answers
224 views

Interpolating a ParametricFunction

Original domain of my independent variable t is 0 to 10 nanometers, but in Mathematica (as in most numerical software), it's good idea to solve differential ...
0
votes
0answers
36 views

Extract x-values from InterpolatingFunction object? [duplicate]

Ok, So I have a numerical solution to a differential equation, and I am trying to get the data points out from it. So far, I have only been able to get the y-values with the following code: ...
0
votes
1answer
78 views
0
votes
1answer
44 views
0
votes
0answers
28 views

Arbitrary precision calculation with NDSolve

I am trying to solve a BVP using shooting method. For this problem I am guessing one initial condition and also a parameter of a ODE. This is why I am not using Mathematica's in built shooting solver. ...
14
votes
1answer
143 views

Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
1
vote
0answers
71 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
6
votes
0answers
69 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
0
votes
2answers
55 views

Plotting direction fields along with trajectories

I am reading "Dynamics and Bifurcations" by Hale and Kocac, and in chapter one the following diagram is shown: Question is, how can I achieve the same plot using Mathematica? I've tried ...
5
votes
1answer
154 views

How to program efficient undershoot/overshoot

I would like to solve the following boundary value problem for $y(x)$ for a fixed value of $k$ between $0 < k <1$: $$y'' + \frac{3}{x} y' - y + \frac{3}{2}y^2 - \frac{k}{2}y^3=0 \\ y'(0) = ...
3
votes
0answers
165 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = ...
4
votes
1answer
116 views

Solving a chemical system using NDSolve

I have to solve a set of coupled differential equations and am not sure how to proceed. It is a model of a chemical process where I'm interested to find the species concentration as $r$ varies. For a ...
2
votes
1answer
501 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
2answers
435 views

Plotting several numerical solutions plus the analytic solution of ODE in one plot

I want to be able to plot several numerical solutions of an ODE, plus its analytical solution in one plot, in order to see how the numerical solutions converge towards the analytical one with respect ...
1
vote
1answer
863 views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
5
votes
1answer
629 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
0
votes
1answer
37 views

Encountered non-numerical value for a derivative at x==0 [on hold]

this may be a duplicate question but I still don't understand how to get around this problem after reading through other posts. I'm trying to solve a differential equation ...
-2
votes
0answers
42 views

Nonlinear eigenvalue problem

I deal with such a equation $$-y''(x) + x^2\cdot y(x) - |y(x)|^2\cdot y(x) = E y(x)$$ where E is eigenvalues with initial conditions: $y(-300) = 0$ and $y(300) = 0$. I want to figure out ...
20
votes
2answers
3k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
1
vote
1answer
112 views

NDSolve and assuming

I am trying to solve the system of PDE with NDSolve and I got an error message like this NDSolve::deqn: "Equation or list of equations expected instead of ...
5
votes
2answers
189 views

Solve wave equation using DSolve?

The wave equation with pined-pined boundary has well-known solutions, but directly input the equation into Mathematica does not return them. $$EI\cfrac{\partial^4 w}{\partial x^4} + ...
1
vote
0answers
31 views

Using an arbitrary area bounded by lines for PDEs?

I have a set of lines I pulled from an image that make a closed loop, pretend it's a unit square for reference. Is there a way to use such an arbitrary region for solving PDEs, and is there a way to ...
0
votes
2answers
45 views

Plotting a Forced Vibration Differential Equation [on hold]

I'm attempting to plot a differential equation solution but mathematica is giving me trouble. The plot is showing up blank. Here is what I have. ...
1
vote
0answers
56 views

Solve PDE with DiracDelta function

This question is related to Solve wave equation using DSolve?. I think it is more appropriate to open another question on this topic. In the question, the compatibility conditions can be introduce ...
3
votes
1answer
172 views

ODE fitting to dataset

So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time. ...
0
votes
2answers
73 views

Setting up two ordinary differential equations [on hold]

Just having a total blank at the moment, I realise that maybe this question would best be suited for a math forum but i assume Mathematica is needed in order to solve these equations. So the question ...
1
vote
2answers
99 views

How to write absolute value and square root in one equation?(runge kutta) [closed]

I got some problem when I run my program. It hangs when I run it. This is my coding for runge kutta Geometric mean(RKGM). ...
4
votes
2answers
3k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
7
votes
2answers
349 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
19
votes
2answers
2k views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
1
vote
1answer
60 views

Trying to find solution for system of ordinary differential Equations [closed]

I've got 2 functions: A'[t] = (0.5/(1 + (B/k1)^n)) - 0.2*A B'[t] = (1/(1 + (A/k2)^n)) - 2*B with conditions of ...
1
vote
1answer
76 views

Diff eqs can be solved?

I'm trying to solve a pair of coupled differential equations, but am having trouble making DSolve evaluate my equations. ...
0
votes
1answer
83 views

nonlinear differential equation

For such a equation $$-y''(x) + x^2\cdot y(x) - |y(x)|^2\cdot y(x) = 0$$ with initial conditions: $y(-500) = 0$ and $y(500) = 0$. I write in mathematica ...
0
votes
0answers
62 views

Eigenvalues of the nonlinear Schrödinger equation [closed]

As an exercise I have to deal with a nonlinear time independent Schrodinger equation eigenvalues and eigenfunction, ...
3
votes
3answers
93 views

Using NDSolve within Manipulate

I'm trying to use NDSolve inside manipulate. Specifically, I have a series of differential equations with coefficients, k1, k2, ...
0
votes
0answers
89 views

Plotting a numerical integration

I have the following code to calculate a numerical integral for any given a: ...
1
vote
0answers
62 views

How to incorporate the boundary conditions into the differentiation scheme in MMA?

Let that we want to numerically solve the following PDE \begin{equation}\label{sde} -r V(S,t)+r S \frac{\partial V(S,t)}{\partial S}+0.5 S^2 \text{sigma}^2 \frac{\partial ^2V(S,t)}{\partial ...
1
vote
1answer
62 views

Power::infy: “Infinite expression 1/0. encountered” (ODE Solution using NDSolve)

While solving the following ode, Eq1 = f'''[x] - f'[x]*f'[x] + f[x]*f''[x] - K1*(2 f'[x]* f'''[x] - f[x]* f''''[x] - f''[x]*f''[x]) - f'[x] == 0 with the ...
0
votes
1answer
62 views

How I can make the StreamPlot of this differential equation?

I need the StreamPlot of this differential equation but I don't know how. dp/dt=0.4p(1 - p/30), 0 <= t < 5 and 0.4p(1 - p/30) - 0.25p, t > 5
-2
votes
0answers
44 views

system of nonlinear partial differential-algebraic equation [closed]

I want to solve 2 coupled partial differential algebraic equations. Below is my program. I am not able to find the solution. Please help for the same. ...
1
vote
1answer
46 views

Unexpected behavior of WhenEvent in NDSolve?

In Mathematica 9.0.1, here is a simple code to numerically solve an initial-value problem: ...
0
votes
2answers
73 views

Plot ParametricNDSolve

I am trying to plot the probability of a molecule being in a certain state via the numerical solution of the Schrödinger's equation of molecule in an oscillating electric field (in a rotating system). ...