Comment on `conservative discretizations of the Kepler motion'
, 2009 We show that the exact integrator for the classical Kepler motion, recently found by Kozlov ({\it J. Phys. A: Math. Theor.\} {\bf 40} (2007) 4529-4539), can be derived in a simple natural way (using well known exact discretization of the harmonic ...
Agarwal R P +8 more
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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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Variable-step finite difference schemes for the solution of Sturm-Liouville problems
, 2014 We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques.
Amodio, Pierluigi, Settanni, Giuseppina
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A novel stochastic ten non-polynomial cubic splines method for heat equations with noise term
Partial Differential Equations in Applied MathematicsIn this paper, a new numerical method for solving a class of stochastic partial differential equations is presented. The proposed method is based on a non-polynomial cubic spline algorithm with an O(h4) local truncation error.
Aisha F. Fareed +2 more
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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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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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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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Uniform convergence on a Bakhvalov-type mesh using the preconditioning approach: Technical report [PDF]
, 2015 The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in the perturbation
Nhan, Thái Anh, Vulanović, Relja
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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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