Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation

Abstract

Second-order Volterra integro-differential equation is solved by the linear barycentric rational collocation method. Following the barycentric interpolation method of Lagrange polynomial and Chebyshev polynomial, the matrix form of the collocation method is obtained from the discrete Volterra integro-differential equation. With the help of the convergence rate of the linear barycentric rational interpolation, the convergence rate of linear barycentric rational collocation method for solving Volterra integro-differential equation is proved. At last, several numerical examples are provided to validate the theoretical analysis.

Linear Barycentric Rational Collocation Method for Beam Force Vibration Equation

“…Cirillo et al [11][12][13][14] have proposed a rational interpolation scheme which has high numerical stability and interpolation accuracy on both equidistant and special distributed nodes. In [15][16][17], integro-differential equation, heat conduction equation, and biharnormic equation are solved by linear barycentric rational collocation method and the convergence rate is proved. In recent papers, Wang et al [18][19][20][21] successfully applied the collocation method to solve initial value problems, plane elasticity problems, incompressible plane problems, and nonlinear problems which have expanded the application fields of the collocation method.…”

A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System

“…At present, various kinds of commercial computing software often fail to give accurate and reliable results for the analysis of frictional contact. erefore, it is very urgent to develop some stable and efficient numerical algorithms [24][25][26][27].…”

Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval

“…ey are easy to include the adaptive feature and can be applied to much difficult integrands [9][10][11]. At the same time, there are numerous works that have been devoted to developing efficient quadrature formulas, such as the Gaussian method [12,13], the Newton-Cotes method [14][15][16], the spline method [17,18], and some other methods [19][20][21][22][23][24][25]. Usually, Gaussian rules have good accuracy if the integrand is smooth, while Newton-Cotes rules are attractive due to their ease of implementation and flexibility of mesh.…”