Computational fluid dynamics (CFD) is a branch of physics that utilizes numerical methods and algorithms to analyze and predict the behavior of fluids and gases under various conditions. This field ...

Two methods are presented for efficiently computing the eigenvalues of the finite-difference Laplacian. One method embeds the region considered in a rectangle. The other method is applicable when the ...

Learn how to solve boundary value problems in Python using the finite difference method! 🐍📐 This tutorial walks you step-by-step through setting up the problem, discretizing the domain, and ...

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Based on multiplicative calculus, the finite difference schemes for the numerical solution of multiplicative differential equations and Volterra differential equations are presented. Sample problems ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

An error analysis of approximation of deltas (derivatives of the solution to the Cauchy problem for parabolic equations) by finite differences is given, taking into ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...

Finite-Difference Time-Domain (FDTD) methods represent a cornerstone in the numerical simulation of wave propagation phenomena. These methods solve Maxwell’s equations directly in the time domain, ...