Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

Abstract

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first-and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

The New Adomian Technique for Solving Singular and Non-singular Partial Differential Equations of First Order

“…transfer, riemannian geometry, applied probability, mathematical physics, and biology [7,10]. Recently, a great deal of interest has been focused on the convergence studies of the series solution obtained using ADM for a wide variety of stochastic and deterministic problems [2,5,9].…”

“…Recently, a great deal of interest has been focused on the convergence studies of the series solution obtained using ADM for a wide variety of stochastic and deterministic problems [2,5,9]. A number of researchers used the ADM method to solve PDEs by ADM. ADM for first order PDEs with unprescribed data [8], some modifications of ADM for nonlinear PDEs [3] , modified decomposition method (MDM) with new inverse differential operators for solving singular nonlinear IVPs in first-and second-order PDEs arising in fluid mechanics [7] and et al The main objective of this paper is to introduce a new technique method for solving singular and non-singular PDEs of the first order.…”