Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle n...

Bending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure is derived using the Galerkin method. The solution was develope based on the classical plate’s theory (CLPT). The reliability ...

This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under idea data-driven methods, algorithms based on Gaussian processes are constructed to solve inverse problem, where we encode distribution information data into kernels ...

A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce two nilpotent Lie algebras and their extended solvable Lie algebras associated with each tree diagram. The solvable tree diagram Lie algebras turn out to be complete Lie algebras of maximal rank analogous to the Borel...