General iterative approximation to differential equations

2023/03/25 by Chang Gao, Gao, Chang
Computer Science · Engineering · Mathematics · #35A01 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2303.14344

openalex publication_date 2023/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain, then using local and global correspondence to transform discrete step function to successive integration on the domain. Numerical scheme is discussed and tested for Navier-Stokes equation.

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