Issue Details

A BRIEF STUDY ON THE NUMERICAL METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

ABSTRACT

The computational efficiency and user-friendliness of the Finite Difference Method (FDM) are two of its defining features. However, its use at large dimensions and with irregular geometries may be difficult. The Finite Element Method (FEM) may be used for issues with large dimensions and non-regular geometries. The downside is that this approach may be quite computationally expensive. Analysing periodic or quasi-periodic solutions is a natural fit for the Spectral Method (SM). The problem is compounded when applying it to non-periodic solutions or irregular geometry. Experts in the nonlinear partial differential equations (NLPDEs) solution should consider these things before deciding on a numerical approach.

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