Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library
Samad Noeiaghdam,
Aliona Dreglea,
Jihuan He,
Zakieh Avazzadeh,
Muhammad Suleman,
Mohammad Ali Fariborzi Araghi,
Denis N. Sidorov,
Nikolai Sidorov
Affiliations
Samad Noeiaghdam
Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia
Aliona Dreglea
Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia
Jihuan He
National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215021, China
Zakieh Avazzadeh
Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China
Muhammad Suleman
Department of Mathematics, Comsats Institute of Information Technology, Islamabad 45550, Pakistan
Mohammad Ali Fariborzi Araghi
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran 1955847881, Iran
Denis N. Sidorov
Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia
Nikolai Sidorov
Institute of Mathematics and IT, Irkutsk State University, Irkutsk 664025, Russia
This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.
