| Summary: | 碩士 === 國立交通大學 === 土木工程系所 === 103 === In the nonlinear related research of the strong form collocation methods, this is the first work using the reproducing kernel collocation method (RKCM) to solve the semilinear elliptic partial differential equations. As for the iteration schemes, we adopt both the quasi-Newton iteration method and Newton iteration method to solve three examples with the following types of solutions: a trigonometric function, an exponential function, and a trigonometric function combined with a polynomial. Based on our numerical results, the two iteration methods show similar convergence behavior. The Newton iteration method converges faster and is more stable than the quasi-Newton iteration method. But the quasi-Newton iteration method requires less CPU time in each iterative step. Therefore, as the number of collocation points increases, the quasi-Newton iteration method will save more time.
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