Questions tagged [differential-equations]

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

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34 views

Need help in finding intersection point of two function in Block environments

Consider the following model, u[x1_, y1_] :=Block[{x = x1, y = y1}, ODE f = Sin[c x + y]; g=(c 5 y + 2)/(x + 2);s1 = Solve[{f == g}];{s1}] and then call the <...
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1answer
52 views

How to tell mathematica polar coordinates belong to mesh?

Context I want to solve a PDE via FEM on a Disk. If I use a Square I can write ...
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1answer
58 views

How can I speed up NDSolve

I have written a simulation that solve a pde, I used a method I found on this site to speed up the calculation but it is still slow. Is there any way to speed up the prosses? ...
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1answer
25 views

Research Explicit Runge-Kutta method / How to find stabiliy function?

I have this initial conditions ...
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3answers
70 views

Solving ODE System and Estimating Parameters with Experimental Data

I am new to Mathematica. I am trying to find out the best-fit values of the parameters appearing in an ODE system of three equations. The three ODE equations are: ...
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0answers
50 views

Simulating a partial differential equation, uniform vegetation and bare soil system (2 species)

I want to simulate a system of two plants ,woody and herbaceous species; with starting condition that half of the grid (square grid) is filled with woody specie, the herbaceous specie exist on the ...
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1answer
47 views

Plot in NDSolveValue

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1answer
40 views

Jacobian and Eigenvalues: is neither a list of replacement rules nor a valid dispatch table, \ and so cannot be used for replacing

I have seen many solutions to this error for finding jacobian and eigenvalues and tried but they are not working for me. Here is the code: ...
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1answer
66 views

Homogeneous linear ODEs with time-dependent coefficient matrix, optimalisation of NDSolve algorithm

I would like to ask for advice on the following (probably not too complicated) problem: I have a linear system of ODEs of the following form: $$ \dot{X}(t) = M(t)X(t) $$ where $ X(t) $ is a vector, ...
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1answer
119 views

archimedian spiral from curvature

I am trying to reconstruct an archimedean spiral from its curvature $$\kappa (\text{s$\_$})\text{:=}\frac{s^2+2}{\left(s^2+1\right)^{3/2}};$$ eqns: $$\left( \begin{array}{c} t'(s)=\frac{\left(s^2+...
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24 views

Coupled differential equation with variable coefficients

Need suggestion to implement and solve this coupled differential equation in mathematica. $\frac{\delta}{\delta t} F_{1}(x,t)=C_1(x,t)F_{1}(x,t)+C_2(x,t)F_{2}(x,t)$ $\frac{\delta}{\delta t} F_{2}(x,...
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Numerical solution of two cupled ODE [duplicate]

I have two coupled differential equations $$\frac{d^2u(x)}{dx^2}=h\;\frac{d^3w(x)}{dx^3}+K\;u(x)$$ $$-EI\;\frac{d^4w(x)}{dx^4}+A\;\frac{d^3u(x)}{dx^3}+q(x)=0$$ and the following boundary conditions: <...
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27 views

Errors in NDSolve for complex matrices

This is the problem. It is quite simple, and looks unwieldy only because I had to rewrite quaternions as complex matrices. ...
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2answers
261 views

Drawing Lines on Differential Equation Slope Field [closed]

I am supposed to create a detailed slope-field for x' = x + t/2 I have made a slope field using: ...
5
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1answer
94 views

Numeric Solution for 1-D ODE with only Neumann conditions

I tried to solve a simple ODE with only Neumann conditions like But obviously this doesn't work. I must add a useless DirichletCondition to make it work I have verified that the solution is correct, ...
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1answer
46 views

How to find the power series solution of this ordinary differential equation using MMA

I already know that the solution of this differential equation $y''(x) - x*y(x) = 0$ can be expressed by the following power series: $$y(x)=c0(1+\frac{x^{3}}{2\times3}+\frac{x^{6}}{2\times3\times5\...
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1answer
70 views

How to solve the differential equation of a Brachistochrone Problem

This is a differential equation to solve the most brachistochrone line, but it can't find the exact analytical solution : ...
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44 views

1D time-dependent Schrödinger equation with absorbing boundary

I'm trying to solve the 1D Schrödinger equation subjected to an absorbing condition using NDSolve but cannot seem to set up the absorbing condition... My problem ...
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34 views

Coupled ODEs: step size is effectively zero; singularity or stiff system suspected

I have seen many solutions to this error and tried but they are not working for me. Here is the code: ...
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0answers
75 views

Solving equations using Implicit-Runge-Kutta method

I am trying to solve the system of equations using Implicit-Runge-Kutta method but mathematica is showing error "NDSolve::ndcf: Repeated convergence test failure at [Tau] == 4.9`; unable to continue."....
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52 views

Small issue with PDE initial condition

I'm trying to solve the Fokker-Planck equation $$\frac{\partial p}{\partial L}(L, \eta)= \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial \eta}(L, \eta)\right] = ...
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43 views

How to solve this system of coupled differential equations (numerically) [duplicate]

I am trying to solve this system of coupled differential equations, code: enter link description here The problem is when I run the code, it appears: NDSolve::ndode: The equations {True} are not ...
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67 views

How to solve numerically this system of coupled differential equations

I am trying to solve this system of coupled differential equations, ...
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1answer
123 views

Help with implemented Piecewise in Module

Suppose we have an ODE in the form: f''[r] + f'[r] == t f[r]+h[r] where ...
5
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1answer
154 views

How to plot trajectories of the Rossler System [duplicate]

This is my current homework problem. I have completed parts a and b, but am now stuck on part c. I'm not sure what it means by plot the trajectories with different initial conditions, nor am I 100% ...
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1answer
113 views

Why can't I solve a system of four third-order partial differential equations using NDSolve?

I solve the problem of optimal control. First, I solve a system of two equations (with respect to the variables p, q, V, n) with already optimal conditions (Kopt and Sopt) to check whether it is ...
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45 views

I want to plot root of the following complex equation

I am trying to plot the roots of the following equation as mentioned in the code below But it is not giving me output. If anyone can resolve this problem for me is most welcome. ...
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1answer
87 views

Using Around with NDSolve

I was trying to obtain the same result of a differential equation with to different methods the first one is based on DSolve and the second one is based on NDSolve ...
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1answer
42 views
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1answer
65 views

Cryptic NDSolve::nlnum when working with matrices

This problem was initially formulated in quaternions, but I had to rewrite them to complex matrices (as they seem to be supported better). Possibly introducing some errors along the way. So the ...
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2answers
87 views

RK4 residual error for ODE

Below I am giving the code that I am using ...
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1answer
80 views

System of pde with Neumann boundary conditions

The Ginzburg-Landau equation for a system of squared superconductor with a slit in presence of a uniform magnetic field can be written as a sort of continuity equation with Neumann boundary conditions ...
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1answer
46 views

how to solve a Partial Differential equations numerically of the kind given below [closed]

eq=D[f[x,y],y]+ f[x,y]/y == Q[x,y] The equation doesn't have any derivative with respect to x. If I use the following syntax for ...
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0answers
44 views

NDSolve and quaternions

I have tried to solve a set of equations of motion in Mathematica and got an error. Then, I simplified it as much as possible, and the following example gives the same error. ...
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44 views

Log plot of residual error for numerical solution of ODE

Below I am giving the code that I am using ...
4
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1answer
157 views

Solve an ODE with parameters in a boundary condition

Consider the ODE: ode = y''''[x] - 2*k^2*y''[x] + k^4*y[x] == I*k*a*((2*x - x^2 - c)*(y''[x] - k^2*y[x]) + 2*y[x]); in which a...
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0answers
117 views

Coupled PDE equation or boundary condition creating singularity issue

Previous post: Using NDSolve and PieceWise for boundary conditions for coupled PDEs I realised that my previous post was a little vague so I hope this post clarifies any confusion. I've looked over ...
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55 views

Solving two ODEs together

Why does Mathematica not give any output when I am trying to use DSolve to solve these two equations? ...
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0answers
37 views

system of pdes equations

Is it possible to solve those group analytically in Mathematica? ...
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0answers
29 views

NDSolve pde with boundary conditions more than equation required

I have a pde which is first order in time and second-order in space. I have a boundary condition in time and two boundary conditions in space at the outer edge; this results in a smooth solution. ...
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2answers
154 views

Why does DSolve fail in this first order differential equation?

I am trying to solve the following first order differential equation: $$ g'(R)=-2 \sqrt{R^2-g(R)}+2 R$$ By direct substitution it can be verified that an obvious solution is $$g(R)=R^2$$ ...
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1answer
40 views

Problem with DSolve, NDSolve with WhenEvent, Boundary Value Problem

I got the same problem as in question: DSolve, NDSolve with WhenEvent Give Incorrect ...
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1answer
54 views

Solving system of partial differential equations

I am solving two PDEs together for two functions y, G: ...
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0answers
38 views

Nesting differential operators

Suppose I define differential operators $d=x\frac{\partial}{\partial x}$ and $L=g(x)d^4$ (so that $L(f)=g(x)(x\frac{\partial}{\partial x})^4f$ ) and I want to expand the differential operator $L=a_0+...
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1answer
66 views

Differential equation with interpolation

If I have a second-order nonlinear differential equation as follow: sol = NDSolve[{*w''[z] - G[z]*w[z] == 0, w'[0] == 100, w[L] == 0.001}, w[z], z] where: <...
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1answer
44 views

Hyperbolic Second Order PDE - boundary condition with sinusoid

This is similar to countless PDE equations, but the error seems specific to my case: I'm trying to solve a hyperbolic PDE, where $U=(x,t)$ and $V=(x,t)$: The system represents a piezoelectric beam ...
6
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1answer
129 views

Updating a graph under ODE dynamics (vertex model)

Consider the following graph, which is obtained from a VoronoiMesh ...
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3answers
574 views

Finding orbits in the Schwarzschild spacetime

I am trying to plot Schwarzschild's orbit without invoking the geodesic equation. As a reference I am using Chandrasekhar's Book (The Mathematical structure of Black Hole, OUP). In page 98 of the ...
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2answers
79 views

Manual ArcLength sampling on spline differs from MeshFunction sampling

Using Michael E2's answer, I performed a manual arclength parameterisation by solving the differential equation (or: finding the inverse of a function whose derivative is known). I compared the ...
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1answer
30 views

How to use conditional clause inside NDSolve

I am trying to solve a differential equation that changes its behaviour depending on the value of the dependent variable. I've tried as shown below, but the computer does not understand my If clause ...

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