Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson’s equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomoge...

Abstract. We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of [6, 7, 4], we propose a probabilistic interpretation of such a P.D.E. in terms of a nonlinear stochastic differential equation driven by a standard Brownian motion. We derive a numerical sch...

This paper investigates the instability of an isotropic, homogeneous, simply supported rectangular plate subjected to a prescribed periodic in-plane load. The material is assumed to be viscoelastic and obey the Leaderman nonlinear constitutive relation. The equation of motion is derived as a nonlinear integro-partial-differential equation, and is simplified into a nonlinear integro-differential...

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanhfunction type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type m...

In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution this equation real kernel ?-harmonic mappings. paper, we study some geometric properties give univalence criteria and sufficient coefficient conditions for mappings that are fully starlike or convex ?, ? [0, 1). Furthermore, establish Landau type theorem

We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. characterize associated model by means generalized action for scalar field, containing higher-derivative terms. The limit obtained considering arbitrarily powers d'Alembertian operator leading to formal infinite-order equation is discussed. general constructed using ex...