Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations
نویسندگان
چکیده
Abstract In this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given conditions is introduced. The collocation method used rational Chebyshev (RC) functions as matrix discretization to treat the ODEs. Rational (RCC) transform problem system of algebraic equations. discussion order convergence RC proposed base specified by its ability deal boundary independent that may tend infinity easy manner without divergence. tested verified two examples, then applied four real life applications models. Also, comparison our results other methods introduced study applicability accuracy.
منابع مشابه
A rational Chebyshev functions approach for Fredholm-Volterra integro-differential equations
The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...
متن کاملRational Chebyshev Collocation Method for Solving Nonlinear Ordinary Differential Equations of Lane-emden Type
Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...
متن کاملA Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...
متن کاملa rational chebyshev functions approach for fredholm-volterra integro-differential equations
the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
ذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2021
ISSN: ['1687-1839', '1687-1847']
DOI: https://doi.org/10.1186/s13662-021-03481-y