TY - JOUR
ID - 103020
TI - Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate
JO - Computational Mathematics and Computer Modeling with Applications (CMCMA)
JA - CMCMA
LA - en
SN -
AU - Yari, Hafez
AU - Delkhosh, Mehdi
AD - Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.
AD - Department of Mathematics and Computer Science,
Bardaskan Branch, Islamic Azad University,
Bardaskan, Iran.
Y1 - 2022
PY - 2022
VL - 1
IS - 2
SP - 35
EP - 45
KW - Non-rectangular domains
KW - 2D integral equations
KW - Jacobi polynomials
KW - Collocation method
KW - Newton-Krylov GMRes algorithm
DO - 10.52547/CMCMA.1.2.35
N2 - In this paper, an applicable numerical approximation has been proposed for solving nonlinear two-dimensional integral equations (2DIEs) of the second kind on non-rectangular domains. Because directly applying the collocation methods on non-rectangular domains is difficult, in this work, at first, the integral equation is converted to an equal integral equation on a rectangular domain, then the solution is approximated by applying 2D Jacobi collocation method, the implementation of these instructions reduces the integral equation to a system of nonlinear algebraic equations, therefore, solving this system has an important role to approximate the solution. In this paper, Newton-Krylov generalized minimal residual (NK-GMRes) algorithm is used for solving the system of nonlinear algebraic equations. Furthermore, an error estimate for the presented method is investigated and several examples confirm the accuracy and efficiency of the proposed instructions.
UR - https://cmcma.sbu.ac.ir/article_103020.html
L1 - https://cmcma.sbu.ac.ir/article_103020_b11f4ccd892fbf09f23f8c31b65638f6.pdf
ER -