SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
سال انتشار: 1390
نوع سند: مقاله ژورنالی
زبان: فارسی
مشاهده: 133
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شناسه ملی سند علمی:
JR_IJMAC-1-1_008
تاریخ نمایه سازی: 2 اسفند 1401
چکیده مقاله:
The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented method is tested with four examples, and the errors in the solution are compared with the existing methods [۱, ۲, ۳, ۴] to verify the accuracy and convergent nature of proposed methods. The RMS errors in the solutions are tabulated in table ۳ which shows that our method can be applied for large values of n, but the maximum n which has been used by the existing methods are only n = ۱۰, moreover our method is accurate and stable for different values of n.
کلیدواژه ها:
Nonlinear Fredholm integral equation ، Cubic B-spline ، Newton-Cotes ، Collocation ، Convergence analysis
نویسندگان
Z. Mahmoodi
Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics
J. Rashidinia
Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics
E. Babolian
Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics