Chebyshev Cardinal Wavelets for Nonlinear Volterra Integral Equations of the Second Kind

Abstract

This study concentrated on the numerical solution of a nonlinear Volterra integral equation. The approach is accorded to a type of orthogonal wavelets named the Chebyshev cardinal wavelets. The undetermined solution is extended concerning the Chebyshev cardinal wavelets involving unknown coefficients. Hence, a system of nonlinear algebraic equations is drawn out by changing the introduced expansion to the predetermined problem, applying the generated operational matrix, and supposing the cardinality of the basis functions. Conclusively, the estimated solution is achieved by figuring out the mentioned system. Relatively, the convergence of the founded procedure process is reviewed in the Sobolev space. In addition, the results achieved from utilizing the method in some instances display the applicability and validity of the method.

Keywords

• volterra integral equation
• chebyshev wavelets
• operational matrix
• convergence
• sobolev space