# Questions tagged [differential-equations]

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

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I wanted to solve the following system of integro-differential equations (IDEs) using finite difference method (FDM). $y_1''(t)+t^2y_1(t)-y_2''(t)+\int\limits_0^t[(t-x)y_1(x)+y_2(x)]\mathrm{d}x=(2+t^... 1answer 43 views ### Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code) I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as where T is the ... 2answers 145 views ### Problem combining ParametricNDSolve with NonlinearModelFit Final Edit: I have found a solution! Specifying Method->"LevenbergMarquardt", Gradient->"FiniteDifference" gives the behavior I am looking for. Huzzah! It appears that the crashing behavior was coming ... 1answer 49 views ### Writing a function that can perform n-times fractional Caputo derivative of order alpha to a function u(x) inductively I wrote this code, but it fails to give the intended answer which is D^(1/2) three times of x^2. any suggestions to correct this code or write a new one. 1answer 41 views ### d-dimensional compiled function in NDSolve Based on this answer, I understand how to use a one dimensional compiled function in NDSolve. Mathematica NDSolve and 'Compile'? I'd like to be able to use a d-dimensional compiled function <... 5answers 714 views ### NDSolve solves this ordinary differential equation only “half-way” This system eqs = {(1/2) Y'[x]^2 == (1 - Log[Y[x]^2]) Y[x]^2, Y == 1} is known to have a simple solution in terms of Gaussian functions, which can be checked ... 0answers 31 views ### Dynamical PDE system tutorials Which are some up-to-date tutorials or books on integrating dynamical PDE systems (involving chaos, Shock waves, etc.) with Mathematica 10.0? 1answer 86 views ### How to solve this partial differential equation for$f$? I want Mathematica to solve for the function$f$.$f$satisfies the following constraints.$\frac{\partial}{\partial x} f(x,y) = y\frac{\partial}{\partial y} f(x,y) = xf(0,0)=0$It would ... 1answer 74 views ### Non-linear ODE from closed-loop system and Response I started using Mathematica 12 and ran into difficulties. Namely, I want to compare the results of the calculation of a closed system from Simulink and in Mathematica. I rummaged around a bit on the ... 0answers 51 views ### Solving an algebraic-differential equation I cannot find the relevant part in the documentation. Maybe you have a quick solution to my problem. Background Sometimes you want to propagate in time some system of ODEs, but not all the variables ... 1answer 71 views ### Update initial conditions recursively/sequentially within ParallelTable using NDSolve I am modelling 3D motion of particles inside a force-field using second-order coupled PDEs, which I solve from time t=t0 to t=t1 with initial conditions x0,y0,z0. I have a total number of "particles" ... 1answer 174 views ### How to solve this differential equation analytically? How can I DSolve the following differential equation? Is there an analytical answer to this equation? ... 1answer 49 views ### Evaluation functions with lower and upper limit ODE? How do I find the numerical value of y at 0 and also at 1. Here is my code. I appreciate any help. ... 1answer 65 views ### NDSolve::ndsv: Cannot find starting value for the variable w I cannot find theNDSolve::ndsv error in this code ... 1answer 67 views ### Matrix of functions I want to create a matrix of functions. As explained in this question, I can create a matrix of variables: ... 0answers 65 views ### 1D transport equation with Neumann conditions I'm trying to solve 2nd order differetntial equation of heat transfer-type in a finite system x<0,L>, in particular: ... 2answers 56 views ### Get the derivative function plot from a NDSolve solution I been trying to plot the derivative function of j[t], being j'[t]. Here a look to the code. I would appreciate your help. Thank you ... 0answers 38 views ### Sensitivity analysis of a hybrid system (using WhenEvent) using ParametricNDSolve [closed] I am trying to do a sensitivity analysis using ParametricNDSolve for a hybrid system. with the following event: ... 0answers 176 views ### DEigenvalues and NDEigenvalues return different values In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ... 1answer 95 views ### why DSolve in V 12 returned an internal module variables with$ on them in this example?

Fyi, Reported to WRI in case it is a bug. [CASE:4288939] Is this supposed to happen? ...
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### Hybrid Systemn Anomalous results while using ParametricNDSolveValue

The hybrid system that I am solving ...
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### One term in non-linear equations prevents NDSolve to work

I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
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### How to vectorize this nonlinear ODE system for NDSolve?

I learned a long time ago that NDSolve can often be sped up by vectorizing systems of equations. I've got a problem now that seems ideal for this approach, but I ...
1answer
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### Cross coupling in DirichletCondition not supported — conflict with documentation?

Mathematica 12.0.0.0 happily solves the trivial coupled differential system as follows: ...
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### InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
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### Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution

I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element. LinearSolve: Linear equation encountered that has no solution. And ...
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### Can we construct our own NDSolveStateData?

NDSolve can be broken into three stages: NDSolveProcessEquations processes the equations and sets up an NDSolveStateData ...
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### Constant positive and negative Gaussian curvature $K$ meridians as orthogonal trajectories

The plot code below depicts two point through which profiles of constant $K$ are drawn positive and negative. ...
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### Reconstructing a function from its gradients

I have a list of the components of the gradients, $\partial f/\partial x_i$, of a function $f(x_1,x_2,\cdots)$. Is there some neat way to reconstruct the function $f$? One approach to doing this ...
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### WhenEvent error in NDSolve ODEs

I wish to change the term, T'[t] to 0 when S[t]<=0 when I solve ODEs. I have used WhenEvent in my NDSolve part, but it seems not work. The code is ...
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### Solving PDE with unreasonable results

I have a simplified version of my chemical reaction problem. Basically it solves the concentration (ca) and grain (g2) diameter. The ca function is depended on particle diameter R, while g2 function ...
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### Solve 1D Wave Equation

I wanna model 1D wave equation and plot it, Here is my try so far, ...
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### Manipulating a ParametricFunction to handle units

I have a pretty nice way to handle units on a result from NDSolve, which basically consists of converting all of the units to SI, stripping them, calling NDSolve, and then putting the units back. I'll ...
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### Line-Dirichlet Boundary NDSolve

I have defined such a Dirichlet boundary conditions which fixes the nodes in a line, however, the results show that only two nodes are fixed, not the nodes in a line, Code: ...
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### DSolve Varying Base on Implementation

I am trying to understand the behavior of a system of equations that is derived from: ...