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

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5
votes
0answers
92 views

unhandled win32 exception in WolframKernel.exe in DSolve of non-linear ODE in one variable

Bug persisting through 10.4. (windows 7, 64 bit) Installed 10.3.1 and started to run some old ode's. in V 9, this ode used to return unsolved, which is ok, but in 10.3.1 now the kernel crashes. ...
7
votes
2answers
127 views

inspecting step size and order of $\tt NDSolve$

I am trying to collect information about what step sizes and what orders is using NDSolve internally. I tried wrapping it into a ...
0
votes
1answer
119 views

Solving ODE system with NDSolve: “singularity or stiff system suspected” [closed]

I'm trying to solve a set of 4 ODEs as specified below, however I'm getting this error ...
1
vote
1answer
196 views

Extracting data from NDSolve result

Normally I wouldn't ask such question before even read the material from the Wolfram Documentation about what I'm trying to do but this time I have a pretty tigh dead end. I apologize for that. So, ...
15
votes
1answer
474 views

Stress calculations using finite elements

A standard engineering problem is to calculate stresses in a structure due to applied forces. With the inclusion of the finite element method in version 10 this question attempts to investigate how ...
1
vote
1answer
90 views

singularity in boundary value problem

I am trying to solve a non linear differential equation with variable parameter. ...
3
votes
1answer
179 views

Finite Elements 3D

Does anyone knows how to solve the Laplace equation in a Sphere domain and with the following boundary conditions: Consider alpha=0. I have tryed the following code, but i don't belive the boundary ...
3
votes
0answers
135 views

How to solve partial differential equation

How to solve in Mathematica this partial differential equation: $0.5\frac{\partial t(x,y)}{\partial x}+1.5\frac{\partial t(x,y)}{\partial y}+t(x,y)=y\cdot \sqrt{1+x^{3}}$ with condition $t(1,y)=y+2$? ...
1
vote
2answers
64 views

ParametricNDSolve and NDSolve inside Manipulate environment

I have a system of three coupled differential equations that can be pretty readily solved by NDSolve: ...
0
votes
0answers
60 views

singularity problem in mathematica [duplicate]

$$ \pmb{\beta [\text{b$\_$},\text{c$\_$}]=\frac{4 c-14}{12 b-6 c-9};}\\ \pmb{\alpha [\text{b$\_$},\text{c$\_$}]=\frac{10-4 b}{12 b-6 c-9};}\\ \pmb{\text{eqn3}[\text{b$\_$},\text{c$\_$},\text{A$\_$}]=\...
5
votes
2answers
111 views

To solve an ode system with pulses

I want to solve an ode system with pulses, for example x'[t] == b*(1 - x[t]) - a*x[t]*y[t], y'[t] == a*x[t]*y[t] - d*y[t] in {t,0,1} and then at the end of ...
5
votes
3answers
154 views

NDSolve divide-by-zero trouble

So I have a set of differential equations (which I know are analytically integrable) but I want to integrate them numerically to get the form of the solution (the solution is not explicit and hence I ...
1
vote
0answers
175 views

Help with calculating a complicated integral

Edit: The question is solved : )) Thank you for your attention ! I am sorry for mass questions, but the question bothers me a lot. So I would like to ask this question here. This problem arises when ...
3
votes
1answer
48 views

solving large number of linear differential equations

I want to solve a large system of 500 by 500 differential equations such that I have equations such as: Note all the A1, A2 are ...
1
vote
1answer
162 views

Solving a system of partial differential equations consist of 6 equations on 9 variables by using Mathematica

I have a system of partial differential equations consist of 6 equations on 9 variables. ...
0
votes
1answer
125 views

how to write this equation In mathematica. where is W is random value either 0 or 1

how to write this equation In mathematica. where is W is random value either 0 or 1. i want to run to certain N=100 I already have ...
0
votes
0answers
25 views

How to use `DSolve` with y'' and y' in the same argument? [duplicate]

I'd like to solve the differential equation $y''(x)=xy'(x)$ in Mathematica. I'm not sure if it can be solved analytically. This is what I have tried: ...
1
vote
0answers
120 views

How to make a parameter stochastic in a differential equation system with NDSolve?

I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
3
votes
1answer
77 views

Find an appropriate algorithm for certain type of first order nonlinear PDE

I am trying to solve a first-order nonlinear PDE of the form $$ \partial_t z(t,x) = f(t, x, z(t,x), \partial_x z(t,x)) $$ with the boundary condition $$ z(0,x) = \phi(x) $$ for some finite domain $x \...
6
votes
2answers
342 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
0
votes
0answers
23 views

Iterating with NDSolveValue in a Do-loop [duplicate]

I am trying to get a differential solution to converge. There are two separate time periods that I am solving for and the entire solution is periodic. I want to use the output from one as the input ...
0
votes
1answer
39 views

Error produced when trying to solve ordinary differential equation [closed]

NDSolve[{x0'[t] == -x0[t]*s*x1^2 + s*x1^2, x1'[t] == x1*s*x1^2, x2'[t] == -x2[t]*s*x1^2, x0[0] == x1[0] == x2[0] == 1}, {x0, x1, x2}, {t, 0, 1}]
3
votes
1answer
84 views

I Need help to solve the differential equation below

I tried to solve the equation using the code below, but got a null solution. If you change the values of p for 2 and alpha to -1.99, a smooth and nonzero solution is obtained. But I need to respect ...
1
vote
1answer
86 views

How can I combine NIntegrate with NDSolve?

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
4
votes
2answers
148 views

Solving parametric ODEs at large parameter values

Question 101668 was not particularly clear and was put on hold for that reason. The author did clarify it a bit, but it seems unlikely that the question will be reopened. Through an exchange of ...
0
votes
2answers
166 views

How can I perform NIntegrate with NDSolve?

I'm a new user and I have no idea how to perform NIntegrate by using NDSolve. For example consider following differential equation (DE): ...
1
vote
0answers
112 views

Problem setting boundary conditions with NDSolve [closed]

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu L_{xx}+...
1
vote
1answer
57 views

Getting Data from Differential Equation Solution

I am solving the following differential equation. I need to get the values of y[x] for x ranging from 1 to 30. I need to get ...
0
votes
1answer
64 views

Shooting method — why is NDSolve giving me an error message?

I am currently trying to write a code to implement the so-called shooting method (I've given a brief description of it below, for those unfamiliar) for second order ODE's in the form $${\mathrm{d}^2y\...
1
vote
1answer
143 views

Why can DSolve not solve this ODE? [closed]

I wish to solve an equation for the field lines of an electric field. This is the textbook question 1.3.8(a) from D. Dubin's Numerical and Analytical Methods for Scientists and Engineers, Using ...
2
votes
1answer
166 views

How to solve $x' = A\cdot x$? [closed]

I want to solve this equation x' = A x in which x' is a 1*18, ...
4
votes
1answer
124 views

StreamPoints adding extra information

Why doesn't the red line start precisely at the defined point $(0, 2)$ and go off to infinity? My initial condition is $(0, 2)$ and I only want to see where that trajectory goes off to. ...
0
votes
1answer
61 views

How can I solve NDSolve with a parameter?

I'm a new user and I have no idea how to solve the equation with a parameter by using NDSolve. For example consider following differential equation (DE): ...
0
votes
0answers
42 views
4
votes
1answer
86 views

DSolve returning InverseFunction while I believe the answer isn't so complicated

I was trying to solve the following differential equation: $$A'(y)^2 = -\frac{1}{l^2} e^{-2A(y)} + \frac{1}{L^2}.$$ I know that one possible answer is $$A(y) = \log\left( \frac{L}{l}\cosh\frac{y}{L}\...
2
votes
1answer
90 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
1
vote
1answer
76 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by NDSolve....
0
votes
3answers
169 views

About a simple differential equation

Just a simple differential equation.Even we can hand to solve it.But the Mathematica give a error. ...
2
votes
1answer
172 views

Solve 2D diffusion equation in polar coordinates

I am trying to solve the diffusion equation in polar coordinates: $\frac{\partial u}{\partial t} = D \left( \frac{\partial^2 u}{\partial r^2} + \frac{1}{r} \frac{\partial u}{\partial r}\right)$ ...
0
votes
1answer
113 views

Mathematica 10.3 Dsolve solving a simple PDE [closed]

I tried to use Mathematica 10.2 and 10.3 to solve this simple PDE and I want to a general solution. But it seems not working. DSolve has been improved in v10.3. But we see it's perhaps not improved ...
2
votes
0answers
89 views

Bypassing a Singularity

I am having trouble trying to solve an ODE that has a singularity when the function M[x]=1. Basically the denominator has ...
0
votes
0answers
107 views

basin of attraction in 3D

I am trying to find a basin of attraction for a 3 dimensional ODE. I am not sure why it isn't working since it worked great for the 2D case. Any help would be much appreciated. My attempt: ...
13
votes
4answers
497 views

periodic boundary conditions and NDEigensystem

Mathematica 10 has a splendid new function, NDEigensystem, that makes it possible to solve Sturm-Liouville problems numerically in a single step. I have not however been able to find a way to get it ...
4
votes
1answer
354 views

Mathematica 10.3 Dsolve solving 2D diffusion PDE

I tried to use Mathematica 10.3 DSolve to solve 2D diffusion PDE with Dirichlet boundary conditions. But it seems not working. Could anyone help check the code? <...
1
vote
0answers
86 views
1
vote
2answers
74 views

NDSolve with one parameter

This is a copyable minimal example to illustrate the problem that occours when I include one parameter U into a differential equation which I want to solve with <...
0
votes
0answers
86 views

How to simplify a messy integrand by integrating by parts

I have a function x[t] and a messy integral over t, containing x[t], ...