Numerical Investigations of the Coupled Nonlinear Non-homogeneous Partial Differential Equations
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
View: 112
This Paper With 11 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_JACM-8-3_024
تاریخ نمایه سازی: 18 اسفند 1400
Abstract:
The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation. The mathematical model is only the first step, however, towards finding the solution of the problem under consideration. It has become possible to develop realistic mathematical models with the currently available computing power for complicated problems in science and engineering. To the best of our knowledge, systematically using the collocation method to acquire the numerical solution has not been previously used for the Klein-Gordon equation. The main aim of this paper is to systematically use the collocation method to acquire the numerical solution of the two coupled nonlinear non-homogeneous Klein-Gordon partial differential equations. We examine and analyze their stability, in detail. To this aim, we use the Von Neumann stability method to show that the proposed method is conditionally stable. A numerical example is introduced to demonstrate the performance and the efficiency of the proposed method for solving the coupled nonlinear non-homogeneous Klein-Gordon partial differential equations. The numerical results demonstrated that the proposed algorithm is efficient, accurate, and compares favorably with the analytical solutions.
Keywords:
Nonlinear coupled hyperbolic Klein-Gordon equations , Nonlinear phenomena , Jacobi collocation method , Stability analysis
Authors
Z.M. Alaofi
Department of Mathematics, College of Science and Arts, King Khalid University, Muhayil Asir, Saudi Arabia
T.A. El-Danaf
Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Medina, Saudi Arabia
Faisal E.I. Abd Alaal
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
S.S. Dragomir
Mathematics, College of Engineering & Science, Victoria University, Melbourne, Australia
مراجع و منابع این Paper:
لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :