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There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving autonomous initial value problems in ordinary differential equations is derived and implemented. The computational...
The hyperplane constrained method has been proposed in Yadani et al. (Appl Math Comp 216:779–790, 2010) computing singular value decomposition (SVD) of matrix. In the method, the SVD is replaced with solving nonlinear systems whose solutions are constrained on hyperplane, and then their solutions are computed with the help of Newton’s iterative method. In this paper, we present a new convergence theorem...
This paper presents meshless method using RBF collocation scheme for the coupled Schrödinger-KdV equations. Instead of traditional mesh oriented methods such as finite element method (FEM) or finite difference method (FDM), this method requires only a scattered set of nodes in the domain. For this scheme, error estimates and stability analysis are studied. L2 and L∞ error norms between the results...
Series expansions of fundamental solutions are essential to algorithms and analysis of the null field method (NFM) and to analysis of the method of fundamental solutions (MFS). For linear elastostatics, new Fourier series expansions of FS are derived, directly from integration. The new expansions of the FS are simpler than those in Chen et al. (J Mech 26(3):393–401, 2010), thus facile to application...
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