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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. [ABSTRACT FROM AUTHOR]

This paper includes four finite element methods which are based on quadratic, cubic, quartic and quintic trigonometric B-spline functions for space discretization and Crank-Nicolson method for time discretization, to be achieved the numerical solution of the Schrodinger equation (SE). The algorithms obtained by different degrees trigonometric B-spline Galerkin methods are new for getting numerical solution of the SE. To see the accuracy of the proposed methods, two numerical experiments are investigated and the comparison of the methods are given in the test problem section. [ABSTRACT FROM AUTHOR]