Results 21 to 30 of about 985 (108)
Alexandria Engineering Journal, 2020 In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations.
Kolade M. Owolabi +2 more
doaj +1 more source
A Laplace decomposition algorithm applied to a class of nonlinear differential equations
Journal of Applied Mathematics, Volume 1, Issue 4, Page 141-155, 2001., 2001 In this paper, a numerical Laplace transform algorithm which is based on the decomposition method is introduced for the approximate solution of a class of nonlinear differential equations. The technique is described and illustrated with some numerical examples.
Suheil A. Khuri
wiley +1 more source
Time parallelization scheme with an adaptive time step size for solving stiff initial value problems
Open Mathematics, 2018 In this paper, we introduce a practical strategy to select an adaptive time step size suitable for the parareal algorithm designed to parallelize a numerical scheme for solving stiff initial value problems. For the adaptive time step size, a technique to
Bu Sunyoung
doaj +1 more source
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
doaj +1 more source
A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$
, 2020 This paper deals with the derivation of an explicit two-stage thirdorder Improved Runge-Kutta Nyström (IRKNG) method for directly solving general second order ordinary differential equations (ODE). This method is twostep and the number of functions to be
Kasim Hussain, F. Ismail
semanticscholar +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
core +1 more source
ANALYTICAL SOLUTION OF BAGLEY TORVIK EQUATION BY GENERALIZE DIFFERENTIAL TRANSFORM
, 2016 In the present paper, we use generalized differential transform method (GDTM) to derive solution of Bagley Torvik equation. The fractional derivative are described in the Caputo sense.
M. Bansal, R. Jain
semanticscholar +1 more source
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
core +1 more source