Abstract
This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs) via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.
Highlights
The past two decades have been witnessing a strong interest among physicists, engineers, and mathematicians for the theory and numerical modeling of integral and integro-differential equations
Nosrati Sahlan completed her PhD in 2013 from Iran University of Science and Technology, Tehran, Iran. She completed her MSc in Applied Mathematics at Iran University of Science and Technology, in 2007 and BSc in Mathematics at University of Shahid Madani Azerbaijan
Nosrati Sahlan has about ten years of research experience in various field of Applied Mathematics such as integral equations, integro-differential equations, wavelets, etc. She has published immense research papers in numerous fields and various international journals of repute like International Journal of Computer Mathematics, Communication in Nonlinear Science and Numerical Simulation, Computational and Applied Mathematics, etc. Her current research interest includes the numerical methods for the solutions of linear and nonlinear Abel’s integral equations
Summary
The past two decades have been witnessing a strong interest among physicists, engineers, and mathematicians for the theory and numerical modeling of integral and integro-differential equations. Nosrati Sahlan has about ten years of research experience in various field of Applied Mathematics such as integral equations, integro-differential equations, wavelets, etc She has published immense research papers in numerous fields and various international journals of repute like International Journal of Computer Mathematics, Communication in Nonlinear Science and Numerical Simulation, Computational and Applied Mathematics, etc. Her current research interest includes the numerical methods for the solutions of linear and nonlinear Abel’s integral equations
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