Numerical solution of parabolic and hyperbolic partial differential equations with nonlocal conditions

Numerical solution of parabolic and hyperbolic partial differential equations with nonlocal conditions

The partial differential equation with an integral condition in one, two or three space dimensions, arises in many physical phenomena. In this paper, we propose a numerical scheme to solve parabolic and hyperbolic equations with classical and integral boundary conditions using collocation points and approximating the solution using radial basis functions (RBFs). This method will be used to reduce the problem to a set of algebraic equations. The results of numerical experiments are presented, and are compared with the results of other methods to confirm the validity and applicability of the presented scheme.

The partial differential equation with an integral condition in one, two or three space dimensions, arises in many physical phenomena. In this paper, we propose a numerical scheme to solve parabolic and hyperbolic equations with classical and integral boundary conditions using collocation points and approximating the solution using radial basis functions (RBFs). This method will be used to reduce the problem to a set of algebraic equations. The results of numerical experiments are presented, and are compared with the results of other methods to confirm the validity and applicability of the presented scheme.