Numerical Techniques for Tackling Non-Boundary Value Problems via Differential Equations

Abstract

Numerical methods play a crucial role in solving differential equations, particularly when dealing with non-boundary value problems (NBVPs). This paper explores various numerical techniques tailored for such scenarios, analyzing their effectiveness and applicability. Beginning with an overview of NBVPs in differential equations, we delve into specific numerical methods including finite difference methods, finite element methods, and spectral methods. Each method's strengths, limitations, and practical considerations are discussed, providing insights into their optimal usage. Case studies and numerical examples further illustrate the application of these techniques in solving real-world problems. Ultimately, this paper aims to provide a comprehensive understanding of numerical methods for tackling NBVPs via differential equations.