Probabilistic collocation method for strongly nonlinear problems: 2. Transform by displacement

An application of differential transform method for solving nonlinear optimal control problems

In this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (OCP's). The approach rest mainly on the differential transform method (DTM) which is one of the approximate methods. The DTM is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. Utilizing this approach, the optimal co...

‎Multistep collocation method for nonlinear delay integral equations

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

SPLINE COLLOCATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS

The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.  

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

On the crack propagation modeling of hydraulic fracturing by a hybridized displacement discontinuity/boundary collocation method

Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...