# Questions tagged [differential-equations]

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

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### Stiff System of ODEs: NDSolve Convergence Issues

I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem. ...
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### NDSolve Inconsistent equation dimensions

I am getting an error while trying to solve for a differential equation. It is saying "NDSolveValue::femper: PDE parsing error... Inconsistant equation dimensions." I was wondering if anyone ...
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### How solve nonlinear equations by 14 unknowns?

This is my code, i want to solve system by 14 equations and 14 unknowns(rr list).But the code doesn't run... ...
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### How to make DSolve express constants in terms of the unknown function [closed]

If I do DSolve[y'[x] == y[x], y[x], x] Mathematica returns {{y[x] -> E^x C}} Is there a way to have it return this ...
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### How to find T[R]?

This is a second question about the system: ...
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### How to set correctly the initial conditions with Infinity?

I have two functions given by the following differential equation system: ...
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### Using RandomVariate in a NDSolve

I want to solve a version of the Langevin's equation using RandomVariante with a normal distribution. Therefore, I used the next code: ...
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### Solving integro-differential equation [closed]

I would like to solve the integro-differential equation of the form $$\left( -n \int_0^b b db + \frac{i \Lambda l_P^2}{9V_c}\frac{d}{db}+b^2+k\right)\psi(b)=0.$$ I followed the steps in Solve an ...
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### NDSolve: input a value for a parameter from a list of values

I have a parameter in an equation which has a different value at each step from a list of values calculated in a former NDSolve differential equation. While what I am trying to achieve is more ...
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### Asymptotic Relation as Boundary Condition

I want to solve a system of non-linear second order differential equations. For some of the unknown functions there are boundary conditions that i know how to write them in Mathematica. One of the ...
131 views

### Mass Transport FEM Using Quad Mesh

This question is a follow-up to my previous question and an attempt to implement @Tim Laska's excellent approach of setting up an anisotropic quad mesh. I'm solving a similar problem to @Tim Laska's ...
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### NDSolve and NIntegrate with parameters

I have a problem with a numeric computation. I should solve a numeric ODE and the rhs is a numeric parametric function that I find with several NIntegrate. I'd like ...
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### problem with solving a simple third order differential equation [duplicate]

I just wrote a simple line of code to solve a third-order differential equation: DSolve[{y'''[x] + 4*y[x]==0, y==1, y'==2, y''==0}, y[x], x] Then ...
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### Solving system of coupled PDEs with method of lines

I'm trying to solve: $\partial _{z} U(z,t) = i \sqrt{d} P(z,t)$ $\partial _{t} P(z,t) = -P(z, t) + i \sqrt{d} U(z,t) + i \Omega_{c}(t)S(z, t)$ $\partial _{t} S(z,t) = i \Omega_{c}(t)P(z, t)$ For the ...
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### ToElementMesh Error/General meshing strategies

I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
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### Periodic extrapolation out of the domain of the solution of a PDE in two directions

As a prototypic problem ...
56 views

### How to plot a system of coupled PDEs using NDSolve [closed]

I am trying to solve the the following system of couples PDEs using NDSolve. However I am struggling to plot the solutions. I am trying to plot |u1[t,x]|^2 (i.e. the square of the absolute value) but ...
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### Integrodifferential equation solving

I am trying to solve a integrodifferential equation in Mathematica, i.e., I'm trying to find a way to evaluate the code below, which isn't yet supported in mathematica, as far as I understand. ...
145 views

### How to solve the wave velocity in steel

In the simulation of stress wave propagation, I have the following two problems. First question: This question comes from page 69 of this book. The Lame equation for a linear elastic body without ...
138 views

### Sensitivity analysis of parameter on eigenvalues of predator-prey model

I am trying to do a sensitivity analysis of the parameter g on the eigenvalues of this simple predator-prey Lotka Volterra model. I know that this code is entirely ...