Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly...

We consider the system of Volterra integro-dynamic equations x(t) = A(t)x(t) + ∫ t t0 B(t, s)x(s)∆s and obtain necessary and sufficient conditions for the uniform stability of the zero solution employing the resolvent equation coupled with the variation of parameters formula. The resolvent equation that we use for the study of stability will have to be developed since it is unknown for time sca...

In recent years, some promising approximate analytical solutions are proposed, such as exp-function method [1], homotopy perturbation method [2 – 11], and variational iteration method (VIM) [12 – 17]. The variational iteration method is the most effective and convenient one for both weakly and strongly nonlinear equations. This method has been shown to effectively, easily, and accurately solve ...

Superhydrophobicity can arise from the ability of a submerged rough hydrophobic surface to trap air in its surface pores, and thereby reduce the contact area between the water and the frictional solid walls. A submerged surface can only remain superhydrophobic (SHP) as long as it retains the air in its pores. SHP surfaces have a short underwater life, and their longevity depends strongly on the...

A Legendre multiwavelet based method is developed in this paper to solve second kind hypersingular integral equation by converting it into a Cauchy singular integro-differential equation. Multiscale representation of the singular and differential operators is obtained by employing Legendre multiwavelet basis. An estimate of the error of the approximate solution of the integral equation is obtai...

where ( ) ( ) + − − − = β α ) ( ) ( ) ( t l t l t M , ( ) ( ) + − − − = ) ( ) ( ) ( t l t l t N α β ; ) (t l is the cumulative default loss at time t ; α and β denote the tranche attachment and detachment points , respectively; ) , ( s t B is the timet price of a pure discount bond maturing at times , and ) , ( s t f the instantaneous forward rate; ω is the payment interval for tranche premium ...

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily handled. We also present some analytical results concerning the spinless Salpeter equation and the action of the square-root operator. 03.65.Pm, 02.30.Rz Typeset us...