On numerical soliton and convergence analysis of Benjamin-Bona-Mahony-Burger equation via octic B-spline collocation

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

“…The quadratic B-spline finite element methods employed to solve the time-fractional Schrodinger equation [29] Furthermore, different authors have developed various methods for solving the governing equation (1.1), like multistep and hybrid methods [30] and a two-step hybrid method [31]. The other methods, such as the Crank-Nicolson scheme [32], quintic Hermite scheme [33], and B-spline collocation technique [34][35][36][37][38][39][40][41], are beneficial to the present scheme. The main goal of the proposed scheme is to obtain a better approximate quantum mechanical energy solution following Schrodinger's original solution and to illustrate how it can be applied to a complex environment with the Schrodinger equation using a nonic B-spline collocation method followed by FEM and the Crank-Nicolson scheme.…”

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.…”