A backward method for transport equation based on Shannon wavelets and characteristics

Abstract

A backward method is proposed to approximate the solution to transport equation at any time instant. With the method of characteristics, values of the solution at selected sampling nodes are obtained by backward tracking along the characteristics. By taking Shannon wavelets as basis functions citing their properties of accuracy in approximation and convenience in construction, the solution is reconstructed by its truncated cardinal serial. Validity and accuracy of the method are demonstrated by numerical examples.