An Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme
نویسندگان
چکیده مقاله:
We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the proposed method.
منابع مشابه
SPLINE COLLOCATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS
The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.
متن کاملAn optimal analytical method for nonlinear boundary value problems based on method of variation of parameter
In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate soluti...
متن کاملSpectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems
and Applied Analysis 3 2. Preliminaries Let w α,β x 1 − x α 1 x β be a weight function in the usual sense for α, β > −1. The set of Jacobi polynomials {P α,β k x } k 0 forms a complete L 2 w α,β −1, 1 -orthogonal system, and ∥ ∥ ∥P α,β k ∥ ∥ ∥ 2 w α,β h α,β k 2 β 1Γ k α 1 Γ ( k β 1 ) ( 2k α β 1 ) Γ k 1 Γ ( k α β 1 ) . 2.1 Here, L2 w α,β −1, 1 is a weighted space defined by L2 w α,β −1, 1 {v : v...
متن کاملA numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method
In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...
متن کاملA New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...
متن کاملA Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems
In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 11 شماره 1
صفحات 35- 42
تاریخ انتشار 2019-01-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023