The Experts below are selected from a list of 28488 Experts worldwide ranked by ideXlab platform
T E Simos - One of the best experts on this subject based on the ideXlab platform.
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optimized three stage implicit runge Kutta Methods for the numerical solution of problems with oscillatory solutions
ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010, 2010Co-Authors: N G Tselios, Z A Anastassi, T E SimosAbstract:We present two new Methods based on an implicit Runge‐Kutta Method of Gauss type which is of algebraic order four and has two stages: the first one has zero dispersion and the second one has zero dispersion and zero dissipation. The efficiency of these Methods is measured while integrating the radial Schrodinger equation and other well known initial value problems.
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an optimized explicit runge Kutta Method with increased phase lag order for the numerical solution of the schrodinger equation and related problems
Journal of Mathematical Chemistry, 2010Co-Authors: A A Kosti, Z A Anastassi, T E SimosAbstract:In this paper we present an optimized explicit Runge-Kutta Method, which is based on a Method of Fehlberg with six stages and fifth algebraic order and has improved characteristics of the phase-lag error. We measure the efficiency of the new Method in comparison to other numerical Methods, through the integration of the Schrodinger equation and three other initial value problems.
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an optimized runge Kutta Method for the solution of orbital problems
Journal of Computational and Applied Mathematics, 2005Co-Authors: Z A Anastassi, T E SimosAbstract:We present a new explicit Runge-Kutta Method with algebraic order four, minimum error of the fifth algebraic order (the limit of the error is zero, when the step-size tends to zero), infinite order of dispersion and eighth order of dissipation. The efficiency of the newly constructed Method is shown through the numerical results of a wide range of Methods when these are applied to well-known periodic orbital problems.
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a fourth algebraic order exponentially fitted runge Kutta Method for the numerical solution of the schrodinger equation
Ima Journal of Numerical Analysis, 2001Co-Authors: T E SimosAbstract:An exponentially-fitted Runge-Kutta Method for the numerical integration of the radial Schrodinger equation is developed. Theoretical and numerical results obtained for the well known Woods-Saxon potential show the efficiency of the new Method.
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a modified phase fitted runge Kutta Method for the numerical solution of the schrodinger equation
Journal of Mathematical Chemistry, 2001Co-Authors: T E Simos, Jesus Vigo AguiarAbstract:A modified phase-fitted Runge–Kutta Method (i.e., a Method with phase-lag of order infinity) for the numerical solution of periodic initial-value problems is constructed in this paper. This new modified Method is based on the Runge–Kutta fifth algebraic order Method of Dormand and Prince [33]. The numerical results indicate that this new Method is more efficient for the numerical solution of periodic initial-value problems than the well known Runge–Kutta Method of Dormand and Prince [33] with algebraic order five.
Jesus Vigoaguiar - One of the best experts on this subject based on the ideXlab platform.
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a fourth order runge Kutta Method based on bdf type chebyshev approximations
Journal of Computational and Applied Mathematics, 2007Co-Authors: Higinio Ramos, Jesus VigoaguiarAbstract:In this paper we consider a new fourth-order Method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the Method may be formulated in an equivalent way as a Runge-Kutta Method having stage order four. The Method thus obtained have good properties relatives to stability including an unbounded stability domain and large @a-value concerning A(@a)-stability. A strategy for changing the step size, based on a pair of Methods in a similar way to the embedding pair in the Runge-Kutta schemes, is presented. The numerical examples reveals that this Method is very promising when it is used for solving stiff initial-value problems.
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an embedded exponentially fitted runge Kutta Method for the numerical solution of the schrodinger equation and related periodic initial value problems
Computer Physics Communications, 2000Co-Authors: G Avdelas, T E Simos, Jesus VigoaguiarAbstract:An embedded exponentially-fitted Runge-Kutta Method for the numerical integration of the Schrodinger equation and the related initial-value problems with periodic or oscillating solutions is developed in this paper. Numerical results show the efficiency of the new Method.
Tobin A. Driscoll - One of the best experts on this subject based on the ideXlab platform.
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A composite Runge-Kutta Method for the spectral solution of semilinear PDEs
Journal of Computational Physics, 2002Co-Authors: Tobin A. DriscollAbstract:A new composite Runge-Kutta (RK) Method is proposed for semilinear partial differential equations such as Korteweg-de Vries, nonlinear Schrodinger, Kadomtsev-Petviashvili (KP), Kuramoto-Sivashinsky (KS), Cahn-Hilliard, and others having high-order derivatives in the linear term. The Method uses Fourier collocation and the classical fourth-order RK Method, except for the stiff linear modes, which are treated with a linearly implicit RK Method. The composite RK Method is simple to implement, indifferent to the distinction between dispersive and dissipative problems, and as efficient on test problems for KS and KP as any other generally applicable Method.
Faqi Liu - One of the best experts on this subject based on the ideXlab platform.
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a nearly analytic symplectically partitioned runge Kutta Method for 2 d seismic wave equations
Geophysical Journal International, 2011Co-Authors: Dinghui Yang, Faqi LiuAbstract:SUMMARY In this paper, we develop a new nearly analytic symplectically partitioned Runge–Kutta (NSPRK) Method for numerically solving elastic wave equations. In this Method, we first transform the elastic wave equations into a Hamiltonian system, and use the nearly analytic discrete operator to approximate the high-order spatial differential operators, and then we employ the partitioned second-order symplectic Runge–Kutta Method to numerically solve the resulted semi-discrete Hamiltonian ordinary differential equations (ODEs). We investigate in great detail on the properties of the NSPRK Method that includes the stability condition for the P–SV wave in a 2-D homogeneous isotropic medium, the computational efficiency, and the numerical dispersion relation for the 2-D acoustic case. Meanwhile, we apply the NSPRK to simulate the elastic wave propagating in several multilayer models with both strong velocity contrasts and fluctuating interfaces. Both theoretical analysis and numerical results show that the NSPRK can effectively suppress the numerical dispersion resulted from the discretization of the wave equations, and more importantly, it preserves the symplecticity structure for long-time computation. In addition, numerical experiments demonstrate that the NSPRK is effective to combine the split perfectly matched layer boundary conditions to take care of the reflections from the artificial boundaries.
G Avdelas - One of the best experts on this subject based on the ideXlab platform.
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an embedded exponentially fitted runge Kutta Method for the numerical solution of the schrodinger equation and related periodic initial value problems
Computer Physics Communications, 2000Co-Authors: G Avdelas, T E Simos, Jesus VigoaguiarAbstract:An embedded exponentially-fitted Runge-Kutta Method for the numerical integration of the Schrodinger equation and the related initial-value problems with periodic or oscillating solutions is developed in this paper. Numerical results show the efficiency of the new Method.
