AN APPROXIMATE SOLUTION FOR DIFFERENT TYPES OF WAVE PROBLEMS

Abstract

In this article, He’s variational iteration method (VIM) is implemented to solve the non-homogeneous dissipative wave, Helmholtz and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary or initial conditions after few iterations. Comparison of the results with those obtained by exact solution and Adomian’s decomposition method reveals that VIM is very effective, convenient and quite accurate to both linear and nonlinear problems. It is predicted that VIM can be widely applied in engineering

Keywords

• Variational iteration method,Helmholtz equation,FKdV equation,nonlinear partial differential equations

DALGA PROBLEMLERİNİN FARKLI TİPLERİ İÇİN BİR YAKLAŞIK ÇÖZÜM

Abstract

Bu makalede, He’nin varyasyonel iterasyon yöntemi (VIM), belli başlangıç koşulları ile homojen olmayan dissipative dalga, Helmholtz ve bazı lineer olmayan beşinci mertebeden Korteweg-de Vries (FKdV) kısmi diferansiyel denklemlerini çözmek için uygulanmıştır. Başlangıç yaklaşımları, birkaç iterasyon sonra başlangıç ve sınır koşullarının uygulanmasıyla belirlenebilen mümkün bilinmeyen sabitler ile keyfi olarak seçilebilir. Analitik çözüm ve Adomian'ın ayrıştırma yöntemi ile elde edilen sonuçların karşılaştırılması, VIM’in çok etkili, uygun ve hem lineer hem de lineer olmayan problemler için oldukça hatasız olduğunu ortaya koymaktadır. VIM’in mühendislikte yaygın olarak uygulanabildiği tahmin edilmektedir.

Keywords

• Varyasyonel iterasyon yöntemi,Helmholtz denklemi,FKdV denklemi,lineer olmayan kısmi diferansiyel denklemler

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