# Tagged Questions

Implicit methods are timestepping methods that use an inversion at every timestep. This allows for much better stability properties than explicit methods, though it comes with a serious speed penalty in some cases. Examples of implicit methods include Backward Euler and Crank-Nicholson.

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### Implicit equation solving COMSOL [closed]

I want to solve a implicit equation in a domain in 1-D geometry. The equation looks like this: i=exp(phi1-phi2-U-i*R) phi1,phi2 are time and space dependent variables. R is a constant. I tried ...
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### Solving the transient heat convection diffusion equation (2D) using BTCS in Matlab with derivative BCs

I'm really stacking guys on how to solve the Solving the transient heat convection diffusion equation (2D) using the full implicit BTCS in Matlab with derivative Boundary condition and variable ...
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### Not getting correct numerical solution for Advection-Diffusion-Reaction eqn

Objective: I am trying to numerically solve $C(x,y,t)$ from the following advection-diffusion-reaction equation in 2D space (x,y) and time. I will be testing my numerical solution with an approximate ...
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### Matlab solution for implicit finite difference heat equation with kinetic reactions

I am trying to model heat conduction within a wood cylinder using implicit finite difference methods. The general heat equation that I'm using for cylindrical and spherical shapes is: Where p is ...
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### Is it possible to solve nonlinear PDEs without using Newton-Raphson iteration?

I am trying to understand some results and would appreciate some general comments on tackling nonlinear problems. Fisher's equation (a nonlinear reaction-diffusion PDE),  u_t = du_{xx} + \beta u ...
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### What is the difference between implicit FEM and explicit FEM?

What is the difference between explicit FEM and implicit FEM exactly? According to the post here, it seems that the only difference is whether implicit or explicit time integration is used. As I ...
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### cuda and numerical methods with implicit time discretization

I am looking to port some code that resolves a set of partial differential equations (PDE) by the finite volume method in IMPLICIT form (for the time discretization). As result there is a tridiagonal ...
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### CFL evolution techniques for Implicit methods

I am working on implicit schemes for Euler equations. Implicit methods allow one to use large CFL values, but is there some way to evolve CFL number from a much smaller value than desired value to ...
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### How to implement Newton's method for solving the algebraic equations in the backward Euler method

Can you explain me how does the backward Euler method works? I have seen the formula and try to understand the method, but what I can't understand is why and how to use the Newton-Rapson method. Do ...
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### Linearized implicit time stepping

Consider the general FD implicit time stepping scheme $\frac{x_{t+1} - x_t}{\Delta t} = f(x_{t+1})$, where $x$ is the vector variable of interest and $f$ is some function, generally non-linear. ...
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### Implicit finite difference schemes for advection equation

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/...
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### Does ADI/Split-operator change the stability properties of the Crank-Nicholson method?

I'm using the Crank-Nicholson method to solve the time-dependent Schrödinger equation with the split-operator method. I'm getting some weird results that are probably the result of a bug somewhere in ...
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### How to obtain an implicit finite difference scheme for the wave equation?

Suppose I had the following problem: $U_{tt}=U_{xx}+U_{yy}$ in $\Omega=[0,1]\times[0,1]$ $U(x,y,0)=f(x,y)$ $U_{t}(x,y,0)=g(x,y)$ $U=0$ on $\partial \Omega$ I know that there is an explicit ...
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### Recommendations for a usable, fast C++ matrix library?

Does anyone have recommendations on a usable, fast C++ matrix library? What I mean by usable is the following: Matrix objects have an intuitive interface (ex.: I can use rows and columns while ...
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### What are the best practices for algorithms and implementation of multi-physics simulations?

Multi-physics simulation involves coupling multiple "physics", often with different space and/or time scales. Additionally, the single-physics codes are often written by different teams. The most ...
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### Can heat distribution in an optical element irradiated by laser be oscillating?

I am modelling a heat distribution in optical element irradiated by laser. System is radially symmetric, and element is thin, i.e. heat value depends only on distance from center. Heat is received via ...