Bivariate Jacobi polynomials for solving Volterra partial integro‐differential equations with the weakly singular kernel

2021 ◽  
Author(s):  
Khadijeh Sadri ◽  
Kamyar Hosseini ◽  
Mohammad Mirzazadeh ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Differential Equations ◽  
Jacobi Polynomials ◽  
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.

scholarly journals Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

2021 ◽  
Vol 6 (1) ◽  
pp. 19
Author(s):  
Mohamed A. Abdelkawy ◽  
Ahmed Z. M. Amin ◽  
António M. Lopes ◽  
Ishak Hashim ◽  
Mohammed M. Babatin
Keyword(s):  
Collocation Method ◽  
Fractional Order ◽  
Jacobi Polynomials ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Singular Kernel ◽  
Variable Order ◽  
Algebraic Equations ◽  
Weakly Singular Kernel ◽  
Weakly Singular

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fractional integral and derivative and fractional-order shifted Jacobi polynomials, the approximate solutions of VO-FIDE-WSK are derived by solving systems of algebraic equations. The superior accuracy of the method is illustrated through several numerical examples.

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