Faraj, Bawar MohammedRahman, Shnyar KarimMohammed, Deni AdnanHilmi, Hozan DlshadAkgul, Ali2024-12-242024-12-2420232705-10642705-1056https://doi.org/10.37256/cm.4320232735https://hdl.handle.net/20.500.12604/8327This 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.eninfo:eu-repo/semantics/openAccessHelmholtz equationinitial boundary value problems (IBVP)finite difference schemecomputational techniquesstability analysisArticle43Q3WOS:001062150900009Q42-s2.0-8517425089610.37256/cm.4320232735