A numerical approach for investigating a special class of fractional Riccati equation
Results in Physics, 2020 A computational scheme for solving special type of fractional Riccati equation with singularly perturbed (FRSP) is investigated. It is based on dividing the equation into algebraic equation and fractional equation.
Bothayna S. Kashkari, Muhammed I. Syam
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Stability analysis of linear multistep methods for delay differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 447-458, 1986., 1986 Stability properties of linear multistep methods for delay differential equations with respect to the test equation 0 < λ < 1, are investigated. It is known that the solution of this equation is bounded if and only if |a| < −b and we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams ...
V. L. Bakke, Z. Jackiewicz
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Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems [PDF]
, 2009 One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself.
Abramovitz +21 more
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Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 4, Page 651-667, 1979., 1979 Linear multistep methods are considered which have a stability region S and are D‐stable on the whole boundary ∂S ⊂ S of S. Error estimates are derived which hold uniformly for the class of initial value problems Y′ = AY + B(t), t > 0, Y(0) = Y0 with normal matrix A satisfying the spectral condition Sp(ΔtA) ⊂ S, Δt time step, Sp(A) spectrum of A ...
Eckart Gekeler
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Numerical comparisons among some methods for Hamiltonian problems
, 2010 We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.Comment: 5 pages, 8 ...
Brugnano, Luigi +2 more
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Numerical treatments of nonlinear Burgers–Fisher equation via a combined approximation technique
Kuwait Journal of ScienceA combined spectral matrix collocation strategy is presented to solve the time-dependent nonlinear Burgers–Fisher equation pertaining to various important physical mechanisms such as advection, diffusion, and logistic reaction.
Mohammad Izadi, Hari Mohan Srivastava
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Enhanced HBVMs for the numerical solution of Hamiltonian problems with multiple invariants
, 2013 Recently, the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient solution of Hamiltonian problems, as well as for other types of conservative problems.
Brugnano, Luigi, Sun, Yajuan
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Efficient implementation of geometric integrators for separable Hamiltonian problems
, 2013 We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of Hamiltonian problems.
Brugnano, Luigi +2 more
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Alexandria Engineering Journal, 2018 In this paper we present a reliable method based on second kind Chebyshev polynomial for the approximate solution of fractional Bloch equation in Nuclear Magnetic Resonance (NMR). The main advantages of the proposed method that it converts the fractional
Harendra Singh, C.S. Singh
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Numerical solution of third order boundary value problems using one-step hybrid block method
Ain Shams Engineering Journal, 2019 Numerical hybrid block methods have been thought to be an appropriate method for solving ordinary differential equation. Therefore, this paper introduces a one-step hybrid block method of order five for directly solving third order boundary value ...
Ra’ft Abdelrahim
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