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B‐spline solution of fractional integro partial differential equation with a weakly singular kernel
Author(s) -
Arshed Saima
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22153
Subject(s) - mathematics , discretization , fractional calculus , collocation method , partial differential equation , mathematical analysis , kernel (algebra) , collocation (remote sensing) , thin plate spline , partial derivative , orthogonal collocation , differential equation , ordinary differential equation , spline interpolation , computer science , statistics , combinatorics , bilinear interpolation , machine learning
The main objective of the paper is to find the approximate solution of fractional integro partial differential equation with a weakly singular kernel. Integro partial differential equation (IPDE) appears in the study of viscoelastic phenomena. Cubic B‐spline collocation method is employed for fractional IPDE. The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order α , 0 < α < 1 . The given problem is discretized in both time and space directions. Backward Euler formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1565–1581, 2017