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

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-5
votes
1answer
86 views

how to change parameters in NDSolve? [closed]

I want to solve a PDE with parameters chosen based on the sign of derivative. For instance in the following PDE ...
7
votes
4answers
744 views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ y_{n}(x):=y_0+\int_{...
0
votes
1answer
159 views

How to make the plot smooth

There are some stranges point which cause the figure isn't smooth. I think that the reason is the method of numericial integration. Here is my code, it's pleasure that one can revise the drawbacks in ...
0
votes
0answers
137 views

PDE: Inconsistent equation dimensions

EDIT: I need to solve the following PDE: $\nabla^2\vec{A}=-\mu_{0}\vec{j}$ where $\vec{j}=\sigma\vec{E}$ and $\sigma=1*10^{10}$ which basically boils down to three different PDE's; $\...
0
votes
1answer
107 views

How to resolve the singularity in NDSolve

I ran into a problem in my Mathematica code. There is a singularity or stiff system in NDSolve. The explicit code is as follows: ...
0
votes
1answer
117 views

Output with NDSolve

I use of the following differential equation: s = NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] Output. The solution in a plot. What is ...
1
vote
2answers
73 views

NDSolve giving NDSolve::deqn: message when given my system of equations [closed]

I am so new on Mathematica. I hope my question is suitable. I have looked the Documentation Center and looked also on StackExchange but I could not handle the problem. It gives always the error ...
4
votes
1answer
186 views

Unexpected results from trying to solve Laplace's equation

I am trying to find the solution to Laplace's equation: $\dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}=0$ over the following region of space: the vertices of the triangle ...
0
votes
0answers
64 views

How do I solve first order non-linear system of PDE: $\partial f^i(x,y)/\partial z = F^i(f^1,f^2,…,f^n)$?

I've previously posted this question in Mathmatics.SE but never receive a response. The old post can be found here: http://math.stackexchange.com/questions/1286495/how-do-i-solve-first-order-non-...
1
vote
0answers
391 views

How can I solve the 2D Laplace equation with Neumann boundary conditions? [closed]

I would like to solve the following boundary value problem for $u(x,y)$: PDE $\quad \quad \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ Domain $\quad \quad 0 \le x \le ...
0
votes
1answer
73 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
0
votes
1answer
161 views

How to solve constraint differential equations using If function

I have to solve a series of differential equations along with a constraint that has to be satisfied at each point of time where $t\in [0, 100]$ The model parameters are ...
11
votes
1answer
276 views

How to specify PDE Boundary condition on Bspline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a ...
12
votes
2answers
195 views

MMA breaks down when `DSolve` -ing a third-order linear ODE

My code is: DSolve[y'''[x] + (x^3 + a^3) y[x] == 0, y[x], x] It should be noted that similar code not only meets the similar problem but also returns more ...
3
votes
2answers
321 views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
-1
votes
1answer
79 views

ParametricPlot not plotting the results I'm getting from NDSolve

I try to plot a phase diagram with ParametricPlot but everytime Mathematica does nothing. I start by ; ...
1
vote
0answers
101 views

How to obtain the magnetic field of the following set up [closed]

This is the experimental set up: A ferromagnetic cylindrical disk (of irrelevant dimensions) has either sides set at different electric potentials (left side at 0 volts and right side at 1 volt). A ...
5
votes
2answers
97 views

How do I programatically set up an NDSolve with lots of equations?

I'd like to set up... NDSolve[x1'[t]==2,x1[0]==0, x2'[t]==2,x2[0]==0, x3'[t]==2,x3[0]==0, x4'[t]==2,x4[0]==0, x5'[t]==2,x5[0]==0, ... etc Can I somehow use x[t,1]...
6
votes
1answer
163 views

Accuracy of Grad-Shafranov PDE's NDSolveValue over implicit region

Context I need to solve for the toroidal flux of the magnetic field above an accretion disc. For this purpose, I define the region over which the flux is non zero, ...
1
vote
1answer
99 views

If[ ] not evaluating properly inside NDSolve[ ]

I am trying to solve a set of equations with the NDSolve. I encounter an error which I try to explain it with the below example. ...
3
votes
0answers
79 views

Verification of results given by NDSolve

I am trying to solve a system of ODEs using NDSolve. The differential equations used are obtained by applying method of lines to actual governing equation. The system includes differential equations ...
0
votes
2answers
106 views

Matrixform ndsolve for mobile robot dynamic equations

Error is: NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded trying to solve for derivatives, so the system will be treated as a system of differential-algebraic equations. You ...
0
votes
1answer
85 views

Ndsolve parametricplot

Ndsolve solution cant manipulate parametric plot!! ...
1
vote
0answers
92 views

Transient PDE with a complex boundary condition [closed]

I am trying to solve a PDE, but one of the boundary conditions is complex, because it includes an integral over the function that I am looking for. The code is shown below ...
1
vote
2answers
150 views

NDSolveValue and DirchletConditions for cylindrical disk

my aim in this is to model the current flow of a cylindrical disk with one end set to potential 0 and the other end set to potential 1. In this section of code I am trying to find the scalar ...
2
votes
1answer
103 views

Problem with NDSolve and Sign

If c1 cnd c2 are zero, the code responds very well; but if one of c1 or ...
0
votes
2answers
87 views

Not seeing line defined in an Epilog option

In the following code, the line defined in Epilog option of my 2nd parametric plot doesn't show up in the content pane of my ...
21
votes
2answers
431 views

Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
2
votes
1answer
216 views

Why does NDSolveValue giving crappy results?

I have been trying out mathematica 10 features, but sadly unable to use NDSolve for even simple PDE's. I am still wrestling with the problem of boundary conditions. The solution I get in the ...
3
votes
1answer
189 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} \displaystyle\left\{\...
4
votes
1answer
340 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
4
votes
0answers
430 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
4
votes
1answer
450 views

Nonlinear PDE solver

I would like to solve the following nonlinear PDE: $$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$ I was trying: ...
7
votes
1answer
198 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
1
vote
1answer
247 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial U}{\...
0
votes
1answer
125 views

NDSolve precision for non-linear ODE with variable initial conditions

I am trying to numerically solve a non-linear ODE with variable initial conditions, specifically it is : $$ \partial_{t}R (r,t) ^2 + 2 R(r,t) \partial_{t} ^2 R(r,t) +r^2 k(r) = 0 $$ and my initial ...
0
votes
1answer
119 views

Variable dependency…easy one

I'm brand new to Mathematica...should be an easy one. Instead of writing u[x] everywhere in the code, how do I assign the dependency early on like this: u=u[x] ...
5
votes
1answer
262 views

How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence ...
0
votes
0answers
75 views

How to extract the time t of an interpolated function created by NDSolve? [duplicate]

I'm working with the function NDSolve. I give it the time of integration, the time I want it to evaluate my differential equations. Sometimes, it crashes before the end of its attribuated time ; For ...
4
votes
1answer
205 views

Specifying NeumannValue for Axial load instead of transverse load (Plane Stress situation)

I am trying to simulate a bar/link element under axial tensile load. The link is of unit thickness and I may use a plane stress model. A plane stress model is an approximation that may be used for ...
0
votes
1answer
101 views

second order nonlinear ode

I need to solve the following equation for $u_n(t)$: $u''=\frac{u'^2}{2u}+\frac{3u^3}{2}+4tu^2+2\left(t^2+\frac{n}{2}+(2p+1)\frac{1+3(-1)^n}{4}\right)u-\frac{n+(2p+1)(1-(-1)^n)}{4u}$ where $p$ is a ...
5
votes
2answers
290 views

FEM giving “ … is not a polynomial error”

Executing the program below I get the ... is not a polynomial error message. I don't have an idea why I am getting this -- any suggestions? ...
-1
votes
1answer
191 views

Solve a differential equation using the power series method

I used the power series method to solve the differential equation y’’+y=0 with y[0]=0 and y’[0]=1 using the following code. In this code “y” is considered as “y = Sum[c[i] x^i, {i, 0, n}] + O[x]^(n + ...
0
votes
1answer
92 views

Solving a simple linear differential equation does not work as advertised [closed]

I have been following examples in an introduction to Mathematica. But the following example regarding a linear differential equation does not work: ...
1
vote
1answer
163 views

Nonlinear boundary value problems for fourth order ordinary differential equations

I am trying to solve a set of equations which are fourth order equations. I want to get the value of w ...
1
vote
1answer
84 views

Ndsolve problem with Sign

Using Sign(...)] in the formulation of my system of ODEs is causing an error that I don't know how to correct. If I use (...) in ...
2
votes
1answer
73 views

Non-autonomous Dynamical system Sliding mode controller Error

This code is a simulation of a sliding mode controller of a non-autonomous dynamic. When I use ArcTan in input, I receive an error. ...
1
vote
0answers
256 views

Solution to heat equation with Neumann boundary conditions and lateral heat loss

I am conducting an experiment on heat conduction in a copper rod. To do so I am using a thin copper rod with several temperature probes, then I am going to compare the data with a solution to the heat ...
3
votes
1answer
124 views

Stopping NDSolver at time of error

I am using NDSolver and WhenEvent to solve a system of differential equations. I get this message: ...
2
votes
1answer
141 views

solve nonlinear equations with NDSolve

I am trying to solve a set of equations with NDSolve. one of them is mg*yg''[t] == NN[t] - kb*yg[t]^1 - cb*yg'[t], When the power of yg[t] is 1 the equations could ...