کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
766986 897140 2012 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions
چکیده انگلیسی

In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann’s boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.


► Numerical solutions of nonlinear parabolic PDE are given using cubic B-spline with SSP-RK3 scheme.
► Numerical solutions of equations have been evaluated without transformation and linearization.
► The presented method needs less storage space that causes to less accumulation of numerical errors.
► The results exhibited by this method are found to be in good agreement with the exact solutions.
► Easy implementation is the strength of this method.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 12, December 2012, Pages 4616–4625
نویسندگان
, ,