This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

The classical theory of optimal control deals with systems governed by ordinary differential equations or, in the case of discrete-time systems, finite difference equations. That basic theory has been extended in many directions: for example, we may have ssystems governed by partial differential equations, systems governed by sets of inequalities that involve partial derivatives, continuous-tim...

We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1 < · · · < qr < 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with...