scholarly journals Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Feras M. Al Faqih
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Error Estimates ◽  
Closed Contour ◽  
Lebesgue Spaces ◽  
Solvability Conditions ◽  
Mechanical Quadrature ◽  
Weakly Singular ◽  
Quadrature Methods ◽  
Singular Integrodifferential Equations

The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.

scholarly journals One-step methods for the numerical solution of linear differential equations based upon Lobatto quadrature formulae

1970 ◽  
Vol 11 (1) ◽  
pp. 115-128 ◽  
Author(s):  
K. D. Sharma
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Gaussian Quadrature ◽  
Physical Systems ◽  
Quadrature Formulae ◽  
Second Order Differential Equations ◽  
Quadrature Methods ◽  
One Step ◽  
Scientists And Engineers ◽  
Linear Differential

The necessity of accurate numerical approximations to the solutions of differential equations governing physical systems has always been an important problem with scientists and engineers. Hammer and Hollingsworth [11] have used Gaussian quadrature for solving the linear second order differential equations. This method has been further developed by Morrison and Stoller [3], Korganoff [1], Kuntzman [9], Henrici [12] and Day [7, 8]. Quadrature methods based upon Lobatto quadrature formulae have recently been considered by Day [6, 8] and Jain and Sharma [10] and seem to give better results.

scholarly journals Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Khadijeh Sadri ◽  
Kamyar Hosseini ◽  
Dumitru Baleanu ◽  
Ali Ahmadian ◽  
Soheil Salahshour
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Chebyshev Polynomials ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Variable Order ◽  
Algebraic Equations ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
Linear Algebraic Equations

AbstractThe shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.

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