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Titlebook: Numerical Analysis and Its Applications; Third International Zhilin Li,Lubin Vulkov,Jerzy Waśniewski Conference proceedings 2005 Springer-

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Andrey B. Andreev,Ivan Todor Dimov,Milena R. Racheva
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Andrey B. Andreev,Jordan T. Maximov,Milena R. Racheva
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High Precision Method for Calculating the Energy Values of the Hydrogen Atom in a Strong Magnetic Ficond-order differential equations. The rate of convergence is examined numerically and is illustrated in the table. The results are in good agreement with the best one up to now and show that 12 significant digits are computed in the obtaining energy values.
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Numerical Treatment of Fourth Order Singularly Perturbed Boundary Value Problemsed solutions to get the solution of the BVP over the entire interval. For the inner regions, the boundary conditions at the end points are obtained through the zero order asymptotic expansion of the solution of the BVP. Examples will be solved to demonstrate the method and its efficiency.
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Splitting Methods and Their Application to the Abstract Cauchy Problemsarallel alternating method, etc.), elaborated to the numerical solution of the abstract Cauchy problem can be interpreted in this manner. Moreover, on the base of this unified approach a sequence of the new methods can be defined and investigated.
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Nodal Two-Dimensional Solitons in Nonlinear Parametric Resonanceerturbations for sufficiently large damping coefficients, they are always unstable to azimuthal perturbations. The corresponding break-up scenarios are studied using direct numerical simulations. Typically, the nodal solutions break into symmetric “necklaces” of stable nodeless solitons.
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