Master of Science (MS)
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In this work, we first discuss solving differential equations by Least Square Methods (LSM). Polynomials are used as basis functions for first-order ODEs and then B-spline basis are introduced and applied for higher-order Boundary Value Problems (BVP) and PDEs. Finally, Kansa's collocation methods by using radial basis functions are presented to solve PDEs numerically. Various numerical examples are given to show the efficiency of the methods.
collocation methods; differential equations; least squares methods; numerical methods
Kazemi, Katayoun Bodouhi, "Solving differential equations with least square and collocation methods" (2015). UNLV Theses, Dissertations, Professional Papers, and Capstones. 2548.