Work

A Space–Time Collocation Method Using the Method of Particular Solutions with Polynomial Basis Functions for Solving the Fisher–KPP Equation

Year: 2025

Type: article

Abstract: The method of particular solutions (MPS) has been widely applied for solving various types of partial differential equations. In this paper, the space–time collocation technique is implemented using MPS with polynomial basis functions (MPS-PBF) to solve the nonlinear Fisher–KPP (Kolmogorov–Petrovsky–Piskunov) equation in both one and two dimensions. The Picard iteration method is used to deal with the nonlinearity of the problem. Four numerical examples are provided, and their results are compared with established methods to demonstrate the effectiveness of the proposed scheme.

Source: Mathematics

DOI: 10.3390/math13213549

Authors: Thir Dangal, Balaram Khatri Ghimire, Anup Lamichhane

Institutions: Augusta University, Alabama State University, Ohio Northern University

Language: English

Topic: Numerical methods in engineering

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4415930219

FWCI: 0.329

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Cited by: 1

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