@Article{cmes.2020.08911,
AUTHOR = {Marjan Uddin, Najeeb Ullah, Syed Inayat Ali Shah},
TITLE = {RBF Based Localized Method for Solving Nonlinear Partial Integro-Differential Equations},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {123},
YEAR = {2020},
NUMBER = {3},
PAGES = {957--972},
URL = {http://www.techscience.com/CMES/v123n3/39300},
ISSN = {1526-1506},
ABSTRACT = {In this work, a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations. The proposed numerical scheme is based on
radial basis functions which are local in nature like finite difference numerical schemes.
The radial basis functions are used to approximate the derivatives involved and the integral
is approximated by equal width integration rule. The resultant differentiation matrices are
sparse in nature. After spatial approximation using RBF the partial integro-differential
equations reduce to the system of ODEs. Then ODEs system can be solved by various
types of ODE solvers. The proposed numerical scheme is tested and compared with other
methods available in literature for different test problems. The stability and convergence of
the present numerical scheme are discussed.},
DOI = {10.32604/cmes.2020.08911}
}