On convergent numerical algorithms for unsymmetric collocation
نویسندگان
چکیده
منابع مشابه
On convergent numerical algorithms for unsymmetric collocation
In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified...
متن کاملStable and Convergent Unsymmetric Meshless Collocation Methods
In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...
متن کاملOn Adaptive Unsymmetric Meshless Collocation
The set Λ consists of infinitely many linear real–valued functionals λ that usually take the form of point evaluations of functions or derivatives at points inside a domain or on some boundary or interface layer. If several differential or boundary operators are involved, we simply put everything into a single set Λ of functionals of various types. We call (1) a generalized interpolation proble...
متن کاملGreedy Unsymmetric Collocation
We present greedy unsymmetric collocation schemes for solving linear elliptic partial differential equations using radial basis functions. The proposed approach circumvents the ill-conditioning problem associated with the standard collocation technique and enables the efficient solution of problems requiring a large set of collocation points. Numerical studies indicate that the accuracy of gree...
متن کاملOn unsymmetric collocation by radial basis functions
Solving partial diierential equations by collocation with radial basis functions can be eeciently done by a technique rst proposed by E. Kansa in 1990. It rewrites the problem as a generalized interpolation problem, and the solution is obtained by solving a (possibly large) linear system. The method has been used successfully in a variety of applications, but a proof of nonsingularity of the li...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2008
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-008-9071-x