Numerical Solution of Volterra Integro-Differential Equations with Linear Barycentric Rational Method

Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation

“…The barycentric formula have been obtained by the Lagrange interpolation formula [8][9][10] and been used to solve Volterra equation and Volterra integro-differential equation [11][12][13][14]. Floater and Kai, Klein and Berrut [15][16][17] have proposed a rational interpolation scheme and get the equidistant node of the barycentric formula.…”

Numerical Solution for Third-Order Two-Point Boundary Value Problems with the Barycentric Rational Interpolation Collocation Method

“…Barycentric rational interpolation not only has high interpolation accuracy on special distributed nodes but also has high interpolation accuracy for equidistant nodes [5][6][7]. is method has been used to solve certain problems such as Volterra integral equations [2,8,9], delay Volterra integrodifferential equations [10,11], plane elastic problems [12], nonlinear problems [13], heat conduction equation [14], and so on [15][16][17].…”

Linear Barycentric Rational Method for Solving Schrodinger Equation

“…For getting the equidistant node of the barycentric formula, Floater [8][9][10] has proposed a reasonable interpolation method; in particular, equidistant distribution nodes and the quasi-equidistant nodes have high numerical stability and accuracy of interpolation [11,12]. In [13,14], the linear barycentric rational collocation method (LBRCM) have been used to solve the integro-differential equation. Wang et al [15][16][17] have expanded the application fields of the collocation method (CM), such as initial value problems, plane elasticity problems, and nonlinear problems.…”