TY - JOUR
T1 - Nonpolynomial Jacobi Spectral-Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind
AU - Huang , Qiumei
AU - Wang , Min
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 927
EP - 951
PY - 2024
DA - 2024/05
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0341
UR - https://global-sci.org/intro/article_detail/aamm/23117.html
KW - Nonpolynomial Jacobi spectral-collocation method, Fredholm integral equations, weakly singular, exponential convergence.
AB - <p style="text-align: justify;">In this paper a nonpolynomial Jacobi spectral-collocation (NJSC) method
for the second kind Fredholm integral equations (FIEs) with weakly singular kernel $|s−t|^{−\gamma}$ is proposed. By dividing the integral interval symmetrically into two parts
and applying the NJSC method symmetrically to the two weakly singular FIEs respectively, the mild singularities of the interval endpoints can be captured and the exponential convergence can be obtained. A detailed $L^∞$ convergence analysis of the numerical
solution is derived. The NJSC method is then extended to two dimensional case and
similar exponential convergence results are obtained for low regular solutions. Numerical examples are presented to demonstrate the efficiency of the proposed method.</p>