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

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0
votes
1answer
90 views

NDSolve in exact points - nonlinear equation (Degrees and Radians confusion)

I found solutions of two nonlinear equations, but I have three small questions. First I am in confusion because of initial value. The system is mechanical and unknown ϕ is an angle, which I set to ...
1
vote
1answer
92 views

Numerically solving an ODE for a parameter

My equation is as follows: sol = ParametricNDSolve[{(f'[r]^2 - 1) f'[r] r == 6.2 (f'[1])^2/1000, f[1] == a}, {f}, {r, 1, 3}, {a}] where the function ...
0
votes
0answers
72 views

Numerical solution of coupled PDEs

First, I wish to solve this system of PDEs: $ u_{tt}-u_{xx}=-6u^5+(8+4a)u^3-(2+4a)u+\frac{2u(v^2-1)^2+bv}{(u^2+c)^2}$ $ v_{tt}-v_{xx}=\frac{4v^3+4v+b}{u^2+c}$ with the initial and boundary ...
0
votes
0answers
41 views

Shooting method problem

I am trying to solve the BVP problem: $ u''-u'=-6u^5+(8+4a)u^3-(2+4a)u, u(0.001)=1, u(10)=-1, u'(0.001)=-0.001$ ...
0
votes
0answers
46 views

Boundary Value Problem- using NDSolve or another method

I am trying to solve a set of coupled partial differential equations, with defined boundary conditions using mathematica. Here are the equations and the boundary conditions. ...
2
votes
2answers
94 views

WhenEvent for several variables

I want to solve a system of nonlinear two differential equations (say, in $\theta(x,t)$ and $\phi(x,t)$ with NDSolve, but I want to stop the evaluation when one of ...
3
votes
2answers
164 views

How to transform transfer functions into differential equations?

is there a way with Mathematica to transform transferfunctions (Laplace) into differential equations? Let's say I have the transfer function $\frac{Y(s)}{U(s)}=\text{Kp} \left(\frac{1}{s ...
0
votes
1answer
63 views

NDSolve Initial Condition Returned as True [closed]

I am attempting to use an NDSolve solution as an initial condition for another NDSolve as suggested in this post: Using NDSolve solution as initial condition for another NDSolve ; however, Mathematica ...
1
vote
2answers
91 views

NDsolve with variable end-point

I want to plot the solution a coupled ODEs as a function of the end point only. Mathematica code: ...
1
vote
1answer
42 views

Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
0
votes
0answers
17 views

NDSolve_ODESolve_Plotsolution [duplicate]

I am trying to use mathematica to solve this problem. Thank you! Given the ODE $$ -\frac{a^2 V_0}{2} f''(x)-V_0\cos\big(\frac{2\pi x}{a}\big) f(x)=E f(x) $$ (a,V_0) are positive real constants. Find ...
2
votes
0answers
56 views

Are there some other ways to solve a second PDE except DSolve?

I have a partial differential equation as follows: $$\frac{\partial p(x,t)}{\partial t}=\text{Dp} \frac{\partial ^2p(x,t)}{\partial x^2}-\frac{p(x,t)-\text{p0}}{\tau }$$ What I try to do was to get ...
0
votes
0answers
96 views

Question about NDSolve

Here is my code: ...
0
votes
1answer
140 views

NDSolve example - analytical vs numerical solution. How to specify initial conditions?

So, I have the following equation: y[t]^-3 == w^2 y[t]/t^2 + y''[t] where w^2 = (t0 k0)^2. Analytic solution is easy to ...
2
votes
1answer
68 views

The output is the same as Input when I add the boundary conditions to a PDE

I am trying to solve a PDE in the first order with specific boundary conditions. When I solve use DSolve without the boundary conditions, Mathematica gives me an answer in an arbitrary function. When ...
2
votes
2answers
366 views

How to visualize slope fields of differential equations without vectors?

I'm looking to visualize slope fields of differential equations for my differential equations course. Every example I see draws them as vectors, adding unnecessary "arrows" that, to me, are visually ...
0
votes
1answer
90 views

Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
0
votes
0answers
75 views

NDSolve::ndsz:At t==0.000039576, step size is effectively zero

I adjusted my code accordinly to the advice I got. However I still have a problem with this code which now looks like this: ...
0
votes
1answer
75 views

Plotting the discrete solution to a PDE

So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space: $$ T_{i}^{n+1}=\left( \dfrac ...
0
votes
0answers
92 views

How to obtain differential equations of motion using Lagrangian dynamics?

I'm confused to find a set of differential equations of motion of a pair of masses, m1 and m2 joined by a spring of constant ...
0
votes
1answer
28 views

How do I pull from a data list for parameter values in a system of ODEs and then solve and plot?

I have a parameter set list and I would like to solve a system of ODEs multiple times using each parameter set in the list. Then I would like each set of solutions to be graphed on the same plot. ...
0
votes
0answers
77 views

Boundary Condition Problem with Green's Function

My temperature distribution looks like: Mean wire temperature is : To[x_] := 2 c1 Cosh[x a1] + a2 And it is continuous at two points. In positive part: ...
0
votes
0answers
42 views

How do you explicitly define Box Operator (D'Alembert operator)? [duplicate]

I wanted to see how one can define a box operator in mathematica? $$ \Box\phi=(-\frac{\partial^{2}}{\partial t^{2}}+\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial ...
0
votes
0answers
70 views

Shooting method for solving 3rd Oder ODE with RK method

This is my 3rd Order IVP. D[y[x], {x, 3}] == (m/2)*((D[y[x], x])^2 - 1) - ((m + 1)/2)* y*(D[y[x], {x, 2}])^2. Initial conditions given are as follows ...
0
votes
3answers
184 views

Find an equations of motion using Euler Eqution [closed]

I am a completely new to Mathematica, so my question and code may look silly. I need to find a equation of motion of a point particle of mass m moving in a potential V(x) = A abs[x]^n. (n=1,2,3,4,5,6. ...
3
votes
1answer
68 views

NDSolve with varying PrecisionGoal and WorkingPrecision

Sometimes we need higher numerical precision to deal with large number cancellation in an equation. But if this cancellation happens only in a small (and known) parameter space, would it be possible ...
5
votes
2answers
240 views

StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
2
votes
0answers
53 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
10
votes
3answers
604 views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
0
votes
1answer
73 views

Setting plot size within vector; dynamic slider (two part question)

I have a question about the size of a plot in mathematica. I'm working on some differential equations (a simplified model of heat transfer in a building). I've programmed it so that you can set ...
0
votes
0answers
30 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
0
votes
1answer
84 views

Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
0
votes
0answers
95 views

How to apply Robin boundary condition in Mathematica

Robin condition is the boundary condition which combines the Dirichlet and Neumann condition at the same boundary. For example: At the boundary x = 0 to 2: I want to apply ...
-1
votes
1answer
51 views

Error message NDSolve::conarg: The arguments should be ordered consistently [closed]

Here is my code, i'm trying to make a simulation of the double pendulum ...
0
votes
0answers
74 views

Maximum of NDSolve output. Problem with interpolating function

I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution ...
0
votes
1answer
116 views

Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
3
votes
1answer
208 views

Solving Rotational Equations of Motion

I'm trying to integrate the rotational equations of motion ...
0
votes
1answer
64 views

Check when DSolve returns input [closed]

I'm making a program where i need to plot the soluton of an ODE and ,if possible, obtain the analytical solution. My idea was to use DSolve, check the output, and if it failed use NDsolve. Now, i ...
4
votes
1answer
208 views

How to solve a system of partial differential equations?

I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c) \\ ...
1
vote
1answer
87 views

Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
0
votes
0answers
40 views

Write nth line to file [duplicate]

I have a code that I am running on a supercomputer. Currently the algorithm must finish before I can export any results from the algorithm. What I would like to do is to have the algorithm write out ...
-1
votes
1answer
112 views

how to solve this ode problem? [closed]

NDSolve::ndnum: Encountered non-numerical value for a derivative at x \ == 0.`. >>
0
votes
1answer
65 views

Cannot get specific value from NDSolve (multiple functions)

I am trying to solve six connected differential equations. This is my code: ...
1
vote
1answer
231 views

Need help with solving a second order differential equation

I need help with solving this differential equation. ...
-1
votes
1answer
79 views

Solve set of non linear differential equations [closed]

I have set of differential equations. For example, I took two equations and tried to solve them as below. I am not getting any results. Please help me to figure it out the mistake. And I wonder if I ...
3
votes
1answer
148 views

Solving a constrained vector system with NDSolve

I'm trying to replicate the pendulum DAE example in the Documentation Center (example/ModelConstrainedSystemsAsDAEs) using Mathematica 9's vector support with NDSolve. So far I have: ...
0
votes
0answers
54 views

Nonlinear System of ODEs

I want to solve this NonLinear System: $$\Theta_{\xi} = \frac{(1-\lambda)K_{\alpha}}{\beta}\Phi^{2}\Theta+\frac{2\beta-1}{6\beta}\xi\Theta$$ $$\Phi_{\xi} = \frac{1}{2\lambda K_{\alpha}\ ...
1
vote
1answer
193 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
1answer
111 views

Mathematica can't find constants for this differential equation

I am having problems solving this differential equation: diffeq = m x''[t] == -a E^(b*x'[t]); sol = DSolve[{diffeq, x[0] == 0, x'[0] == v0}, x[t], t] The output ...
0
votes
1answer
82 views

Partial differential equation with initial conditions

And so I want to solve the following equation, subject to these initial conditions: $\ u_{tt} - u_{xx} = 6u^5+(8+4a)u^3-(2+4a)u$ $\ u(0,x)=\tanh(x), u_t(0,x)=0$ When I use NDSolve to solve within ...