Efficient Finite Difference Approaches for Solving Initial Boundary Value Problems in Helmholtz Partial Differential Equations

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Tarih

2023

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Universal Wiser Publisher

Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

This study presents numerical solutions for initial boundary value problems of homogeneous and non-homogeneous Helmholtz equations using first- and second-order difference schemes. The stability of these methods is rigorously analyzed, ensuring their reliability and convergence for a wide range of problem instances. The proposed schemes' robustness and applicability are demonstrated through several examples, accompanied by an error analysis table and illustrative graphs that visually represent the accuracy of the solutions obtained. The results confirm the effectiveness and efficiency of the proposed schemes, making them valuable tools for solving Helmholtz equations in practical applications.

Açıklama

Anahtar Kelimeler

Helmholtz equation, initial boundary value problems (IBVP), finite difference scheme, computational techniques, stability analysis

Kaynak

Contemporary Mathematics

WoS Q Değeri

Q3

Scopus Q Değeri

Q4

Cilt

4

Sayı

3

Künye