Frontiers

Editorial: Approximation methods and analytical modeling using partial differential equations

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...
Scientific Research Publishing

Velazquez, G.L. (2012) Partial Differential Equations of First Order and Their Applications to Physics. World Scientific Publishing Company.

ABSTRACT: Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, ...
Scientific Research Publishing

Evans, L.C. (2022) Partial Differential Equations. American Mathematical Society.

ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...
IEEE

On the Solutions of a Fifth Order Nonlinear Partial Differential Equation of Fluids

Abstract: This paper studies a fifth order nonlinear partial differential equation that describes nonlinear waves in fluids and oceans. Exact solutions are obtained for this equation using the ...
IEEE

A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations

Abstract: In this paper, we introduce a reduced order Iterative Linear Quadratic Regulator (RO-ILQR) approach for the optimal control of nonlinear Partial Differential Equations (PDE). The approach ...
Frontiers

Finite difference schemes for MHD mixed convective Darcy–forchheimer flow of Non-Newtonian fluid over oscillatory sheet: A computational study

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order ...