A novel method with convergence analysis based on the Jacobi wavelets for solving a system of two-dimensional Volterra integral equations

ABSTRACT

The main objective of this paper is to introduce a collocation-based method for solving a system of two-dimensional Volterra integral equations. The proposed approach is based on the Jacobi wavelets collocation procedure. In addition, the Gegenbauer wavelets method has been implemented to show the comparison of error norms obtained by the proposed method. This proposed approach is applied to reduce the system of Volterra integral equations into a system of algebraic equations. Furthermore, some theorems are elucidated to establish the convergence analysis of the proposed method. Some numerical problems are presented in order to show the accuracy and effectiveness of the proposed scheme. Furthermore, comparison tables and some figures are depicted in support of numerical analysis of the proposed scheme.

KEYWORDS:

• System of two-dimensional
• Volterra integral equations
• Jacobi wavelets
• Gegenbauer wavelets
• collocation method

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65R20
• 45D05
• 65T60
• 65M70

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author acknowledges the financial support under the scheme ‘Innovation in Science Pursuit for Inspired Research (INSPIRE)’ fellowship vide Grant No. IF170719.