Numerical Solution of a Class of Nonlinear Boundary Value Problems arising in Chemical Industry

In this work a new approach based on cubic B-spline wavelets and Galerkin method is presented for numerical solution of some nonlinear boundary value problems which arise in modeling a tabular adiabatic chemical reactor. First utilizing the operational matrix of derivative of B-spline wavelets, the unknown function and its derivatives are approximated by cubic B-spline wavelets with unknown coefficients. Thus the nonlinear boundary value problem transforms to a sequence of linear equations. For solving the obtained system, Galerkin method is applied with dual of cubic B-spline scaling and wavelets as weighting functions. Some properties of B-spline wavelets such as semi orthogonality and having compact support and vanishing moments cause that the operational matrix of method be very sparse. For showing the accuracy of the method some test problems are given and findings are compared with theresults of some other methods for numerical solving of this class of equations.

Keywords:

Cubic B-spline wavelets , dual functions , Operational matrix of derivative and integration , Galerkin method