Hyperbolic Partial Differential Equations with Nonlocal Mixed Boundary Values and their Analytic Approximate Solutions

摘要

Partial differential equations of hyperbolic type when considered with mixed Dirichlet/Neumann constraints as well as nonlocal conservation conditions model many physical phenomena. The prime motivation of the current work is to apply the recently developed meshfree method to such differential equations. The scheme is built on series expansion of the solution via proper base functions akin to the Galerkin approach. In many cases, the simple polynomials are adequate to convert the hyperbolic partial differential equation and boundary conditions of nonlocal kind into easily treatable algebraic equations concerning the coefficients of the series. If the sought solutions are polynomials of any degree, then the method has the ability of resolving the equations in an exact manner. The validity, applicability, accuracy and performance of the method are illustrated on some well-analyzed hyperbolic equations available in the open literature.