An adaptive stepsize algorithm for the numerical solving of initial-value problems
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 The present paper focuses on the efficient numerical solving of initial-value problems (IVPs) using digital computers and one-step numerical methods. We start from considering that the integration stepsize is the crucial factor in determining the number ...
Militaru Romulus
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An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model
Advances in Applied Mathematics and Mechanics, 2018 The blood flow model admits the steady state, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme ...
Shouguo Qian
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Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
, 2010 We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete gradient schemes and
Cieśliński, Jan L. +1 more
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Distribution functions of Poisson random integrals: Analysis and computation [PDF]
, 2010 We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral $I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds)$, where $N$ is a Poisson random measure with control measure $n$ and $\krnl$ is a suitable kernel ...
Taqqu, Murad S., Veillette, Mark S.
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Demonstratio MathematicaThis article investigates new analytical wave solutions within the beta (β\beta ) fractional framework (Fκ\kappa IIAE and Fκ\kappa IIBE) of the Kuralay II equations, which are significant in the field of nonlinear optics.
Ege Serife Muge
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Linear rational finite differences from derivatives of barycentric rational interpolants [PDF]
, 2012 Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences.
Berrut, Jean-Paul, Klein, Georges
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A One Step Method for the Solution of General Second Order Ordinary Differential Equations [PDF]
, 2012 In this paper, an implicit one step method for the numerical solution of second order initial value problems of ordinary differential equations has been developed by collocation and interpolation technique.
Adesanya, A. A. +2 more
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Finite difference schemes on quasi-uniform grids for Bvps on infinite intervals
, 2014 The classical numerical treatment of boundary value problems defined on infinite intervals is to replace the boundary conditions at infinity by suitable boundary conditions at a finite point, the so-called truncated boundary.
Fazio, Riccardo, Jannelli, Alessandra
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Performance analysis of SSE and AVX instructions in multi-core CPUs and GPU computing on FDTD scheme for solid and fluid vibration problems [PDF]
, 2014 In this work a unified treatment of solid and fluid vibration problems is developed by means of the Finite-Difference Time-Domain (FDTD). The scheme here proposed takes advantage from a scaling factor in the velocity fields that improves the performance ...
Beléndez Vázquez, Augusto +6 more
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Local accuracy and error bounds of the improved Runge-Kutta numerical methods
Journal of Applied Mathematics and Computational Mechanics, 2018 In this paper, explicit Improved Runge-Kutta (IRK) methods with two, three and four stages have been analyzed in detail to derive the error estimates inherent in them whereas their convergence, order of local accuracy, stability and arithmetic complexity
S. Qureshi +2 more
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