Numerical solution of second order linear hyperbolic telegraph equation

This paper is of about a numerical solution of the second order linear hyperbolic telegraph equation. To solve numerically the second order linear hyperbolic telegraph equation, the cubic B-spline collocation method is used in space discretization and the fourth order one-step method is used in time discretization. By using the fourth order one-step method, it is aimed to obtain a numerical algorithm whose accuracy is higher than the current studies. The efficiency and accuracy of the proposed method is studied by two examples. The obtained results show that the proposed method has higher accuracy as intended.This work has been supported by the Scientific Research Council of Eskisehir Osmangazi University under project No. 2018-2090.Publisher's Versio

KdV DENKLEMİ İÇİN KUİNTİK B-SPLİNE GALERKİN METODU

Korteweg de Vries (KdV) denklemi, Crank Nicolson parçalanması ile birlikte kuintik B-spline şekil ve taban fonksiyonlarının kullanıldığı Galerkin sonlu elemanlar metoduyla yaklaşık olarak çözülmüştür. Bir solitonun yayılması ve iki solitonun çarpışmasını içeren iki klasik test problemi kullanılarak önerilen yöntemin doğruluğu kontrol edilmiştir.  Sonuç olarak önerilen yaklaşık yöntemin KdV denkleminin sayısal çözümü için faydalı bir yöntem olduğu görülmüştür

B-spline collocation methods for numerical solutions of the Burgers' equation

Both time- and space-splitted Burgers&#39; equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers&#39; equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers&#39; equation. The results of both schemes are compared for some test problems.</p

B-spline collocation methods for numerical solutions of the Burgers' equation

Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems

Quintic B-spline Collocation Method for Numerical Solutions of the RLW Equation

Quintic B-spline collocation schemes for numerical solution of the regularized long wave (RLW) equation have been proposed. The schemes are based on the Crank–Nicolson formulation for time integration and quintic B-spline functions for space integration. The quintic B-spline collocation method over finite intervals is also applied to the time-split RLW equation and space-split RLW equation. After stability analysis is applied to all the schemes, the results of the three algorithms are compared by studying the propagation of the solitary wave, interaction of two solitary waves and wave undulation. doi:10.1017/S144618110800007

Quintic B-spline collocation method for numerical solution of the RLW equation

Quintic B-spline collocation schemes for numerical solution of the regularized long wave (RLW) equation have been proposed. The schemes are based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The quintic B-spline collocation method over finite intervals is also applied to the time-split RLW equation and space-split RLW equation. After stability analysis is applied to all the schemes, the results of the three algorithms are compared by studying the propagation of the solitary wave, interaction of two solitary waves and wave undulation

A High Order Accurate Numerical Solution of the Klein-Gordon Equation

In this paper, numerical solution of the nonlinear Klein-Gordon equation is obtained by using the cubic B-spline Galerkin method for space discretization and the finite difference method which is of order four for time discretization. Accuracy of the method is presented by computing the maximum error norm. Robustness of the suggested method is shown by studying some classical test problems

A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS

In this paper, numerical solution of the advection-diffusion equation is obtained by using extended cubic B-spline functions. For space discretization, the extended cubic B-spline Galerkin method is used to integrate the advection-diffusion equation and for time discretization, the Crank-Nicolson method is employed to obtain the fully integrated advection-diffusion equation. The maximum error norm has been used to show the accuracy of the method. Robustness of the suggested method is shown by studying some classical test problems and comparing the results with some earlier ones