Numerical solution of nonlinear ordinary differential equations using flatlet oblique multiwavelets

Abstract

This paper is concerned with the construction of a biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. The system is then used to solve nonlinear ordinary differential equations. The biorthogonality and high vanishing moment properties of this system result in efficient and accurate solutions. Finally, numerical results for some test problems with known solutions are presented and the absolute errors are compared with the errors resulting from B-spline bases.

Keywords:

• operational matrix of derivative
• flatlet
• oblique multiwavelets
• biorthogonal system

2000 AMS Subject Classifications :

• 65T50
• 65L10
• 65M70