The conventional Fourier coefficient asymptotic expansion is derived by means of a specific contour integration. An adjusted expansion is obtained by deforming this contour. A corresponding adjustment to the Euler-Maclaurin expansion exists. The effect of this adjustment in the error functional for a general quadrature rule is investigated. It is the same as the effect of subtracting out a pair...

The nonlinear equations of mathematical physics are major subjects in physical science [1]. Recently many new approaches for finding the exact solutions to nonlinear wave equations have been proposed, for example, tanh-sech method [2–4], extended tanh method [5–7], sine-cosine method [8–10], homogeneous balance method [11, 12], Jacobi elliptic function method [13–16], F -expansion method [17–19...

The paper deals with Euler'sand Taylor's expansion methods for next numerical solution in Matlab environment. There are many applications in technical practise described and modelled by linear or non-linear differential equation (DE) systems. A fictitious exciting functions method makes possible numerical solution of this DE system with non-stationary matrices. The solution of examples with non...

Some new generalized solitary solutions of the Klein–Gordon–Schrödinger equations are obtained using the Exp-function method, which include some known solutions obtained by the F-expansion method and the homogeneous balance method in the open literature as special cases. It is shown that the Exp-function method is a straight, concise, reliable and promising mathematical tool for solving nonline...

The effective field theory approach simplifies the perturbative computation of ground state energy diluted gas fermions allowing in case unpolarized system to easily re-derive classic results up $(k_{\rm F}a_0)^2$ order (where $k_{\rm F}$ is system's Fermi momentum and $a_0$ $s$-wave scattering length) (with more labour) extend it F}a_0)^4$. corresponding expansion polarized spin $1/2$ known an...

in this work g'/g-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. it is shown that g'/g-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...

Blasius boundary layer solution is a Maclaurin series expansion of the function \(f(\eta)\), which has convergence problems when evaluating for higher values \(\eta\) due to singularity present at \(\eta\approx-5.69\). In this paper we are introducing an accurate \(f(\eta)\) using Taylor's expansions with progressively shifted centers expansion(Leaping centers). Each solved as IVP three initial...

The copper oxide (CuO) nanowires/functionalized graphene (f-graphene) composite material was successfully composed by a one-pot synthesis method. The f-graphene synthesized through the Birch reduction chemistry method was modified with functional group "-(CH₂)₅COOH", and the CuO nanowires (NWs) were well dispersed in the f-graphene sheets. When used as anode materials in lithium-ion batteries, ...