Linear Barycentric Rational Collocation Method for Beam Force Vibration Equation

Abstract

The linear barycentric rational collocation method for beam force vibration equation is considered. The discrete beam force vibration equation is changed into the matrix forms. With the help of convergence rate of barycentric rational interpolation, both the convergence rates of space and time can be obtained at the same time. At last, some numerical examples are given to validate our theorem.

Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation

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Linear barycentric rational collocation method for solving telegraph equation

“…Floater et al [26][27][28][29][30] have proposed a rational interpolation scheme which is numerically stable and has high interpolation accuracy on both equidistant nodes and Chebyshev points of the second kind. In recent papers, linear barycentric rational collocation methods [31][32][33][34] have been used to solve the integro-differential equation, heat conduction equation, beam force vibration equation, and biharmonic equation. Wang et al [35][36][37] successfully applied the barycentric interpolation collocation method to solve initial value problems, plane elasticity problems, incompressible plane problems, and nonlinear problems.…”

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“…ese research studies extended the application fields of barycentric rational collocation method. In recent papers, Li et al [23][24][25][26][27] have used the barycentric rational collocation method to solve heat conduction equation, biharmonic problem, and second-order Volterra integro-differential equation.…”