The mGFD (meshless Generalized Finite Differences) repository provides a comprehensive solution for numerically solving Partial Differential Equations in two dimensions on highly irregular regions.

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 ...

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ABSTRACT: The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the ...

ABSTRACT: This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space (FTCS) finite difference scheme. The ...

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Abstract: Maxwell's equations are transformed through discretisation of the solution domain using Finite Difference Method (FDM) to a system of algebraic equations referred to as finite difference ...

Abstract: The unconditionally stable (US) Chebyshev (CS) finite-difference time-domain (FDTD) method is extended for solving the problems of long-time simulation or harmonic resonance using a ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...