# Questions tagged [pde]

Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.

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### Effect on methods like Crank-Nicolson of adding a potential term, changing heat equation to Schrodinger equation

I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...
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### Euler Explict Method for solving the PDE for option prices under the Schwartz mean reverting model. Numerical Finance

I have to solve the following PDE for a Call option : $\partial_tV + \{ \alpha - (\mu - \lambda/ \alpha -log(S))\}S\partial_SV + 1/2 \sigma^{2}S^{2}\partial_{S}^{2}V - rV = 0$ Where V(S,t) is the ...
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Let define a predictor step for the equation $\frac{\partial u}{\partial t}+\frac{\partial f}{\partial x}=0$, by: $$U_{i+\beta}^{n+\alpha} \equiv \bar{U}_{i}=U_{i}^{n}+\beta\left(U_{i+1}^{n}-U_{i}^{n}\... 0answers 14 views ### How to modify or add continuity condition for internal boundary in COMSOL? [closed] Using pressure acoustics module in COMSOL, I’m modeling the acoustic pressure in two domains: air and liquid droplet, where acoustic waves move from air to the liquid droplet. The air domain has the ... 1answer 87 views ### I need help with a variational formulation For this problem \begin{cases} &\frac{d^2 u}{dx^2}=Log(1+x+y),in \quad\Omega=(0,1)^2\\ &u=0,\qquad on \quad\Gamma_{1}: x=0\\ &u=0,\qquad on \quad\Gamma_{3}: x=1\\ &\frac{du}{d\eta}=0,\... 0answers 66 views ### Numerical scheme to calculate the normal mode of a set of hyperbolic PDEs? I would like to solve the linearised, ideal, MHD equations, where the gas pressure is zero.$$\frac{\partial u_x}{\partial t}=v_A^2(x,z)\left[\nabla_{||}b_x - \frac{\partial b_{||}}{\partial x}\right],...
I have a differential system like this, where $\Phi$ is a scalar valued unknown function: $$\nabla\Phi = \left(f_1(x, y), f_2(x,y)\right)^T$$ I'm trying to solve it in a FEM solver (COMSOL ...