In this paper, we examine the space discretization of time fractional telegraph equation (TFTE) with Mamadu-Njoseh orthogonal basis functions. For ease and convenience, we deal with the fractional derivative by first converting from Caputo's type to Riemann-Liouville's type. The proposed method was constrained to precise error analysis to establish the accuracy of the method. Numerical experimentation was implemented with the aid of MAPLE 18 to show convergence of the method as compared with the analytic solution.

In this paper, a new approach called Power Series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.

This work is aim at providing a numerical technique for the Volterra integral equations using Galerkin method. For this purpose, an effective matrix formulation is proposed to solve linear Volterra integral equations of the first and second kind respectively using orthogonal polynomials as trial functions which are constructed in the interval [ ] 1,1 − with respect to the weight function () w x x 2 1 = +. The efficiency of the proposed method is tested on several numerical examples and compared with the analytic solutions available in the literature.

This paper presents Tau-collocation approximation approach for solving first and second orders ordinary differential equations. We use the method in the stimulation of numerical techniques for the approximate solution of linear initial value problems (IVP) in first and second order ordinary differential equations. The resulting numerical evidences show the method is adequate and effective.

The role of fractional differential equations in the advancement of science and technology cannot be overemphasized. The time fractional telegraph equation (TFTE) is a hyperbolic partial differential equation (HPDE) with applications in frequency transmission lines such as the telegraph wire, radio frequency, wire radio antenna, telephone lines, and among others. Consequently, numerical procedures (such as finite element method, H 1 -Galerkin mixed finite element method, finite difference method, and among others) have become essential tools for obtaining approximate solutions for these HPDEs. It is also essential for these numerical techniques to converge to a given analytic solution to certain rate. The Ritz projection is often used in the analysis of stability, error estimation, convergence and superconvergence of many mathematical procedures. Hence, this paper offers a rigorous and comprehensive analysis of convergence of the space discretized time-fractional telegraph equation. To this effect, we define a temporal mesh on with a finite element space in Mamadu-Njoseh polynomial space, , of degree An interpolation operator (also of a polynomial space) was introduced along the fractional Ritz projection to prove the convergence theorem. Basically, we have employed both the fractional Ritz projection and interpolation technique as superclose estimate in -norm between them to avoid a difficult Ritz operator construction to achieve the convergence of the method.