Pseudo-Laplace transform is an important notion from pseudo-analysis’ framework that is often used in dealing with differential or integral equation. The (⊕, ̄)-Laplace transform considered here is a generalization of the pseudo-Laplace transform based on a special class of generalized pseudo-operations that need not be commutative nor associative. This pseudo-Laplace type transform has been use...

We consider the Laplace transform as a Henstock-Kurzweil integral. We give conditions for the existence, continuity and differentiability of the Laplace transform. A Riemann-Lebesgue Lemma is given, and it is proved that the Laplace transform of a convolution is the pointwise product of Laplace transforms.

in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

The Laplace-Green's function methods of Paper I are extended to describe polymers confined in interacting, impenetrable cylindrical geometries, whose treatment is far more challenging than the slit and box geometries considered in Paper I. The general methods are illustrated with calculations (as a function of the polymer-surface interaction) of the free energy of confinement, the radial densit...

The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential equation. After applying the Laplace transform, a new cost functional is constructed and a variational problem is formulated. The key feature of this functio...

New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GRmethod consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GRmethod pr...

We study the asymptotic form of the Gopakumar–Vafa invariants at all genus for Calabi–Yau toric threefolds which have the structure of fibration of the An singularity over P. We claim that the asymptotic form is the inverse Laplace transform of the corresponding instanton amplitude in the prepotential of N = 2 SU(n + 1) gauge theory coupled to external graviphoton fields, which is given by the ...

It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical...

i=1 (∆− μiI)vk = h(x), x ∈ <+, μi > 0, ( ∂vi ∂xn + snvi)xn=0 = φi(x ′ ), x ′ = (x1, ...xn−1) ∈ a; and we obtain for h(x)≡ 0 a relation between the inverse Laplace transforms v k,2m(x ′ , sn) and solutions of a similar problem to (1) in x ′ ∈ 0 instead of μi, and then using inverse tabular t...