In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis ...

We discuss the problem of detecting the location of discontinuities of derivatives of a periodic function, given either finitely many Fourier coefficients of the function, or the samples of the function at uniform or scattered data points. Using the general theory, we develop a class of trigonometric polynomial frames suitable for this purpose. Our methods also help us to analyze the capabiliti...

In this study, trigonometric quintic B-spline collocation method is constructed for computing numerical solutions of the reaction-diffusion system (RDS). Schnakenberg, Gray-Scott and Brusselator models are special cases systems considered as examples in paper. Crank-Nicolson formulae used time discretization generalized RDS nonlinear terms time-discretized form linearized using Taylor expansion...

Abstract— This paper describes the use of GC quadratic trigonometric spline interpolant for preserving the shape of monotonic data. Simple data dependent constraints are derived for shape parameters to preserve the monotonicity through monotonic data. The necessary and sufficient conditions for the monotonicity of the trigonometric quadratic interpolant have been derived. The scheme is computat...

A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...