2020
DOI: 10.1002/num.22539
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Abstract: The linear barycentric rational collocation method for solving heat conduction equation is presented. The matrix form of discrete heat conduction equation by collocation method is also obtained. With the help of convergence rate of the barycentric interpolation, the convergence rate of linear barycentric rational collocation method for solving heat conduction equation is proved. At last, several numerical examples are provided to validate the theoretical analysis.

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Cited by 35 publications
(13 citation statements)
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References 16 publications
(18 reference statements)
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“…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.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…. , n, and 2 Shock and Vibration C (4) ij � r (4) i x j , C (2) ij � r i ″ x j , D (2) ij � r i ″ t j , (16) are the elements of the differentiation matrices with…”
Section: Introductionmentioning
confidence: 99%
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%