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SUPERVISOR
Amir Hashemi,Mehdi Tatari varnosfaderani
امیر هاشمی (استاد مشاور) مهدی تاتاری ورنوسفادرانی (استاد راهنما)
 
STUDENT
Jaleh Nouri
ژاله نوری

FACULTY - DEPARTMENT

دانشکده ریاضی
DEGREE
Master of Science (MSc)
YEAR
1387
: In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. Radial basis functions from a primary tool for multivariate interpolation. Some of the most commonly used radial functions feature a shape parameter, allowing them to vary from being nearly flat ( mall) to sharply peaked ( large). The former limit can be particularly accurate when interpolating a smooth function based on scattered data. Linear combinations of radial basis functions (RBFs) can provide very good interpolants for multivariate data. Multiquadric (MQ) basis functions, generated by , have proven to be particularly successful. The radial basis functions method is meshfree, easy to implement in any number of dimensions and spectrally accurate for certain taypes of radial functions. Approximation of derivatives used to be practical only on highly regular grids in very simple geometries. Since radial basis function (RBF) approximations permit this even for multivariate scattered data, there has been much recent interest in practical algorithms to compute these approximations effectively.The generalization of compact FD formulas that we propose for scattered nodes and radial basis function achieves the goal of still keeping the number of stencil nodes small nodes small without similar reduction in accuracy
: در این پایان نامه ابتدا به درون یابی با استفاده از توابع پایه شعاعی می پردازیم و سپس با استفاده از درون یابی فرمول های تفاضلات متناهی را به دست آورده و آن ها را برای حل عددی معادلات با مشتقات پاره ای خطی وغیر خطی استفاده می کنیم. جواب تقریبی چند معادله ی خطی و غیر خطی لاپلاس و گرما را به دست آورده و در نهایت پایداری و همگرایی این روش ها را بررسی خواهیم کرد

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