Questions tagged [finite-difference-method]
Tag for the usage of "FiniteDifference" Method embedded in NDSolve and implementation of finite difference method (fdm) in mathematica.
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How to Set Precision for an RSOLVE Problem
The following code was working fine -- now it produces errors. I originally built this in ver 13.1 and I'm now running ver 14. I think I'm getting machine precision errors after k=11 that were not ...
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Solving a large number of coupled non-linear equations
I would like to numerically have a solution of the Gross-Pitaevskii equation for an impurity coupled with a 1D weakly interacting bosonic bath, given by:
\begin{align}
i\frac{\partial \phi_0(x,t)}{\...
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Reaction diffusion equation
I have an issue when I run this code which illustrates the 2D Fisher KPP equation for boundary condition u=0 and initial condition is equal to 1 if (x,y)=(0,0) and0 otherwise , isue finite diffrence ...
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How to constrain two PDE variables to be the same value on boundary?
I have a 4 pdes for 4 variables: v, v2, ua, and p. I would like to specify that v==v2 on the left and right boundaries at all times. Here are the equations:
I discretise the system using PDEtoODE. ...
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Finite difference method in 2D [closed]
We look for $u(x, y, t)$ satisfying
$$
\frac{\partial u}{\partial t}=\lambda_1 \frac{\partial^2 u}{\partial x^2}+\lambda_2 \frac{\partial^2 u}{\partial y^2}+\mu u(1-u), \quad t>0, \quad(x, y) \in \...
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NDSolve does not satisfy initial and boundary condition
I am using NDsolve to solve for a coupled pde system $vA[x,t]$ and $vU[x,t]$.
I have initial condition for $vU[x,0]=2$,
and the boundary condition as $\partial_x vU(0,t)=1$. I have accounted for these ...
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NDSolve does not take into account the boundary condition
I am using the following script to solve a coupled pde.
I get the error "NDSolve has computed initial values that give a zero residual for the
differential-algebraic system, but some components ...
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Solving system of coupled pdes with Neuman and Drichlet Bc
I am trying to solve a system of coupled PDEs. However, I have issues assigning initial and boundary values to the unknown field. I have checked and initial values satisfy the boundary conditions, and ...
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Solving coupled quasi-linear PDEs with boundary conditions
I realized that in this solution, changing one of the boundary conditions makes the answer invalid. I wonder if it is possible to modify the code in this answer to solve the following equations.
$$ \...
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How do I couple an 1D PDE to a 2D Laplace equation?
Recently I've come across the following system governing the spreading of an evaporating droplet. The height of the droplet $h$ is defined by the following equation
$$\frac{\partial h}{\partial t}=-\...
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Problem with calculation of Lyapunov exponent
The code given by Chris K for Lyapunov Exponent does not work and gives lot of errors for the dynamical system given in equation(2) of this paper
The dynamical equations:
...
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Numerical Solution for a Non-Linear Functional Fractional Differential Equation (FFDE)
I tried solve non-linear Functional-Fractional Differential Equation (FFDE) with this method, but it works on only for range: $x\in \{0,1\}$.
I what extend the solution range for example for general ...
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Two-directional vibration of Euler–Bernoulli beam with Lagrange multiplier
Background
I'm going to investigate a beam-pendulum coupling system (in this question I won't consider the pendulum though), that is, a spherical pendulum is suspended on the tip of a cantilever beam. ...
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How to improve FDM solver for unsteady viscous flow?
To solve the problem that is discussed in the paper Finite Difference Analysis of Time-Dependent Viscous Nanofluid Flow Between Parallel Plates we developed FDM solver based on the code from the blog ...
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Method of lines - Dirichlet and mixed BC
I have a dissolution problem to solve with two equations (everything is in dimensionless form - concentration, time and distance - EDIT: that came from the second Fick's law, where the distance was ...
