Sameeha Raad
@uqu.edu.sa
Department of Mathematical Sciences
Umm Al-Qura University
EDUCATION
Ph.D. in Applied Mathematics (Integral Equations and Elasticity)
Umm Al-Qura University: Makkah, SA
MScs. in Applied Mathematics (Integral Equations and Numerical Analysis)
Umm Al-Qura University: Makkah, SA
Bachelor's Degree in Mathematics
King Abdulaziz University: Jeddah, SA
RESEARCH INTERESTS
Integral equation, Elasticity, Numerical Analysis
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Sameeha Raad and Khawlah AlQurashi
New York Business Global LLC
In this paper, the Volterra-Fredholm integral equation is derived from a linear integro-differential equation with a fractional order 0 < α < 1 using Riemann–Liouville fractional integral. The existence and uniqueness of the solution are proved using the Picard method. Popular numerical methods; the Toeplitz matrix, and the product Nystr ̈om are used in the solution. These methods will prove their effective in solving this type of equation. Two examples are solved using the mentioned methods and the estimation error is calculated. Finally, a comparison between the numerical results is made.
M. A Abdou and S. A Raad
American Scientific Publishers
M. A Abdou and S. A Raad
American Scientific Publishers
In this paper, the existence of a unique solution of the nonlinear quadratic integral equation (NQIE) of the second kind with continuous kernels, under certain conditions, is considered. Then, Adomian Decomposition Method (ADM) and new modifications have been considered to obtain a nonlinear algebraic system (NAS), where the existence of a unique solution of this method is also, proved. Finally, numerical results are computed when the continuous kernels take some different forms. Moreover, the rate of convergence error, in each case, is computed.