The regularizing properties of multistep methods for first kind Volterra\n integral equations with smooth kernels

2016/04/29 by Robert Plato, Plato, Robert
Mathematics · #65R30 #Differential Equations and Boundary Problems #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1604.08703

openalex publication_date 2016/04/29 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

We study quadrature methods for solving Volterra integral equations of the\nfirst kind with smooth kernels under the presence of noise in the right-hand\nsides, with the quadrature methods being generated by linear multistep methods.\nThe regularizing properties of an a priori choice of the step size are\nanalyzed, with the smoothness of the involved functions carefully taken into\nconsideration. The balancing principle as an adaptive choice of the step size\nis also studied. It is considered in a version which sometimes requires less\namount of computational work than the standard version of this principle.\nNumerical results are included.\n

Related

• Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations
• A class of monotonicity-preserving variable-step discretizations for Volterra integral equations and time fractional ordinary differential equations
• Numerical solution of Volterra integral equations of the first kind with discontinuous kernels
• The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data
• Numerical Study of Index-v First kind Volterra Integral Equations as Ill-posed Problem