Bernstein series solution of a class of linear integro-differential equations with weakly singular kernel

2011 ◽  
Vol 217 (16) ◽  
pp. 7009-7020 ◽  
Author(s):  
Osman Raşit Işik ◽  
Mehmet Sezer ◽  
Zekeriya Güney
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Singular Kernel ◽  
Weakly Singular Kernel ◽  
Weakly Singular

scholarly journals Second-order time discretization with finite-element method for partial integro-differential equations with a weakly singular kernel

1999 ◽  
Vol 40 (4) ◽  
pp. 513-524
Author(s):  
Chang Ho Kim ◽  
U Jin Choi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Time Discretization ◽  
Second Order ◽  
Singular Kernel ◽  
Element Approximation ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
Element Method

AbstractWe propose the second-order time discretization scheme with the finite-element approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the finite element method and the time discretization is based on the Crank-Nicolson scheme with a graded mesh. We show the stability of the scheme and obtain the second-order convergence result for the fully discretized scheme.

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