Smoothing transformation and spline collocation for weakly singular Volterra integro-differential equations

2017 ◽  
Vol 114 ◽  
pp. 63-76 ◽  
Author(s):  
T. Diogo ◽  
P.M. Lima ◽  
A. Pedas ◽  
G. Vainikko
Keyword(s):  
Differential Equations ◽  
Spline Collocation ◽  
Weakly Singular ◽  
Smoothing Transformation

scholarly journals Spline Collocation for Multi-Term Fractional Integro-Differential Equations with Weakly Singular Kernels

2021 ◽  
Vol 5 (3) ◽  
pp. 90
Author(s):  
Arvet Pedas ◽  
Mikk Vikerpuur
Keyword(s):  
Differential Equations ◽  
Special Choice ◽  
Spline Collocation ◽  
Numerical Illustration ◽  
Weakly Singular Kernels ◽  
Local Boundary ◽  
Weakly Singular ◽  
Regularity Properties ◽  
Singular Kernels ◽  
Non Local

We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study the existence, uniqueness and regularity of the exact solution. Based on the obtained regularity properties and spline collocation techniques, the numerical solution of the problem is discussed. Optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented.

scholarly journals Numerical study of thermal radiation and mass transfer effects on free convection flow over a moving vertical porous plate using cubic B-spline collocation method

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
M. Abu zeid ◽  
Khalid K. Ali ◽  
M. A. Shaalan ◽  
K. R. Raslan
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Thermal Radiation ◽  
Porous Plate ◽  
Convection Flow ◽  
Spline Collocation ◽  
Free Convection Flow ◽  
B Spline ◽  
Vertical Porous Plate

Abstract In this paper, we present a numerical method based on cubic B-spline function for studying the effects of thermal radiation and mass transfer on free convection flow over a moving vertical porous plate. Similarity transformations reduced the governing partial differential equations of the fluid flow to a system of nonlinear ordinary differential equations which are solved numerically using a cubic B-spline collocation method. The effects of various physical parameters on the velocity, temperature, and concentration distributions are shown graphically, and the numerical values of physical quantities like skin friction, Nusselt number, and Sherwood number for various parameters are presented in tabular form and discussed.

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