The localizedmethod is one of the popular approaches in solving large-scale problems in science and engineering. In this paper, we implement the localized method of particular solutions using polynomial basis functio...
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In this paper, two localized meshless methods based on polynomial basis functions are utilized to solve axisymmetric problems. In the first approach, we applied the localized method of particular solutions (LMPS) and ...
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In this paper, two localized meshless methods based on polynomial basis functions are utilized to solve axisymmetric problems. In the first approach, we applied the localized method of particular solutions (LMPS) and the closed-form particular solution to simplify the two-stage approach using Chebyshev polynomial as the basis functions for solving axisymmetric problems. We also propose the modified local Pascal polynomial method (MLPM) to compare the results with LMPS. Since only the low order polynomial basis functions are used, no preconditioning treatment is required and the solution is quite stable. Four numerical examples are given to demonstrate the effectiveness of the proposed methods.
In recent years, localizedmethods are proven to be very effective for solving various types of problems in scientific computing. Many researchers have successfully implemented localized approaches to solve large-scal...
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