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

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1answer
55 views

Piecewise Function within NDSolve

So I am quite new to Mathematica and programming in general and I am running into an issue while trying to use the numerical diff eq solver (NDSolve) within mathematica. This is what my code looks ...
2
votes
1answer
143 views

NDSolve doesn't work for this simple differential equations

I try to use NDSolve to do this partial differential equations, but the result is wrong... The source term is a Gaussian pulse as time and an exponential decay with the depth z. The result should be ...
2
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1answer
106 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
9
votes
1answer
680 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
1
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1answer
44 views

Multiplying two parametric solutions

I'm solving two (1-parameter) differential equations and I want to plot the product of their solutions, how do I do this? Here's the code, ...
3
votes
0answers
73 views

Unknown (internal?) function with `DSolve`

I am solving With Mathematica 10 the following ODE system: DSolve[{B'[x] == -f[x]*Cos[l]*G[x], G'[x] == +f[x]*Sin[l]*B[x]}, {B,G}, x] The solution is almost ...
0
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1answer
71 views

Solving differential equation with Variable constans?

How do I solve the following differential equations using Mathematica under the assumptions: If Abs[r[t]]<50 ->A=0.5;B=2; AND ...
0
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1answer
112 views

Solving differential equation with initial conditions

I want to solve the following differential equation with initial conditions: ...
1
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1answer
94 views

Generating a boundary mesh from a list of points

I have a list of points from which I am trying to generate a mesh: ...
1
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1answer
62 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 ...
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1answer
57 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
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2answers
227 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
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0answers
38 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
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1answer
111 views
15
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1answer
200 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
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0answers
92 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 ...
0
votes
2answers
62 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
162 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
175 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
127 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
527 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
438 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
899 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
638 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 ...
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
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1answer
125 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
230 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
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0answers
35 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
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2answers
48 views

Plotting a Forced Vibration Differential Equation [closed]

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
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0answers
66 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 ...
5
votes
1answer
194 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
78 views

Setting up two ordinary differential equations [closed]

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
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2answers
115 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
375 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
65 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
81 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
134 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 ...
3
votes
3answers
111 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
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0answers
91 views

Plotting a numerical integration

I have the following code to calculate a numerical integral for any given a: ...
1
vote
0answers
79 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
82 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 ...
1
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1answer
48 views

Unexpected behavior of WhenEvent in NDSolve?

In Mathematica 9.0.1, here is a simple code to numerically solve an initial-value problem: ...
1
vote
2answers
82 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). ...
0
votes
1answer
70 views

Problem using NDSolveValue

Good afternoon, fellas. Could anyone here help me solve this problem? ...
0
votes
0answers
75 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...