We solve the time-dependent Dirac equation for a muon which is initially bound to a fissioning actinide nucleus. The computations are carried out on a 3-D cartesian lattice utilizing the Basis-Spline collocation method. The muon dynamics is sensitive to the nuclear energy dissipation between the outer fission barrier and the scission point. From a comparison with experimental data we find a dis...

Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and  L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...

Collocation method with sixth degree B-splines as basis functions has been developed to solve a fifth order special case boundary value problem. To get an accurate solution by the collocation method with sixth degree B-splines, the original sixth degree B-splines are redefined into a new set of basis functions which in number match with the number of collocation points. The method is tested for...

A computational study of five finite element methods for the solution of a single second order linear ordinary differential equation subject to general linear, separated boundary conditions is described. In each method, the approximate solution is a piecewise polynomial expressed in terms of a B-spline basis, and is determined by solving a system of linear algebraic equations with an almost blo...

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalarand vector-valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resultingmethod combines the favorable properties of isogeometric collocation and the geometrical and a...

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differential Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT) are developed for the solution of the QSC equations. The complexity of the FFT solvers is O(N2 logN), where N is the gridsize in one dimension. These direct...

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...