In the present paper, a comprehensive review of the different techniques used for solving the
Burgers equation has been presented along with the recent progress going in finding its …

A multivariable technique has been incorporated for guesstimating solutions of Nonlinear
Partial Differential Equations (NPDE) using bases set of B-Polynomials (B-polys). To …

Fractional-order partial differential equations have gained significant attention due to their
wide range of applications in various fields. This paper employed a novel technique for …

In this article, we present a novel B-Polynomial Approach for approximating solutions to
partial differential equations (PDEs), addressing the multiple initial conditions. Our method …

Dynamics of a particle in confined-harmonic potential, subjected to external static electric
and time-dependent laser fields is studied. The energy levels and wave functions of …

A two-variable process to estimate results of Hyperbolic Partial Differentiation (HPD)
equations in a B-Polynomial (B-Poly) bases is established. In the proposed process, a linear …

We extend the formalism of nth order Darboux transformations to the time-dependent
nonhomogeneous Burgers equation (NBE) in (1+ 1) dimensions. Similar to the Schrödinger …

This paper proposes a higher order implicit numerical scheme to approximate the solution of
the nonlinear partial differential equation (PDE). This equation is a simplified form of Navier …

A method to construct approximate solutions for a quantum mechanical system has been
introduced in a Bernstein-polynomial (B-polynomial) basis. The B-polynomial-Galerkin …

This thesis uses B-Polynomial bases to solve both one-dimensional and multidimensional
linear and nonlinear partial differential equations, as well as linear and nonlinear fractional …