Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics

Abstract

In the present study, the complex valued Schrodinger equation (CVSE) is solved numerically by a nonic B-spline finite element method (FEM) in quantum mechanics. The approach employed is based on collocation of nonic B-splines over spatial finite elements so that we have continuity of the dependent variable and its first eight derivatives throughout the solution range. For time discretization Crank-Nicolson scheme of second order based on FEM are employed. The method

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

“…Similarly various integral transforms [25,26] are implemented to solve higher order partial differential equations. Also various new soliton solution approaches are investigated; like Sardar sub-equation technique [27], multi soliton solution of Vakhnenko-Parkes equation [28], Coke price prediction approach [29], multivariate stochastic volatility models by using optimization mechanisms [30], Galilean transformation of Schrodinger equation [31], bifurcation analysis of Hindmarsh-Rose model [32] etc B-spline collocation [33][34][35] and the block method [36,37] are additional techniques that improve the current article and are advantageous to the existing system.…”

Explicit and Implicit Numerical Investigationof One-Dimensional Heat Equation Based on Spline Collocation and Thomas Algorithm

“…Integral boundary conditions with finite difference scheme [8,9]and cubic Hermite B-spline techniques [10]are used to solve the heat equation. The methods based on B-spline collocation technique [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] are beneficial to the present manuscript. The highlights of the present topic is the application of spline collocation method approach, to obtain approximate solution to one dimensional parabolic equation on explicit and implicit version.…”