One-dimensional heat and advection-diffusion equation based on improvised cubic B-spline collocation, finite element method and Crank-Nicolson technique

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.…”

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.…”

Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

“…This type of PDE is also studied by Singh et al, [14] in the form of reaction-diffusion equation using trigonometric Bspline with Neumann and Dirichlet boundary conditions. Jena and Senapati [15] presented solution of heat and advection-diffusion equation using improvised cubic B-spline collocation, finite element method and Crank-Nicolson technique but these methods have high arithmetic computations, lower accuracy, and complexity in computer programming. Goh and Ismail [16] used cubic b-spline collocation for the solution of heat and wave equation but to sustain accuracy smaller space steps are needed.…”