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The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are appl...
In this paper, we presented an initial value approach for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right). By employing asymptotic pow...
A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domain...
Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), i...
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
Abstract: Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere $S$ with smooth characteristic initial data, a theorem of Rendall shows that the vacuum E...
Physicists have used billiards to understand and explore both classical and quantum chaos. Recently, in 2001, a group at the University of Texas introduced an experimental set up for modeling the wedg...
In this paper, we present a symbolic algorithm for solving a class of nth order linear or nonlinear ordinary differential equations with initial conditions. This algorithm is based on Laplace Adomian ...
series of high-resolution numerical experiments, augmented by theory, to further explore the dynamics of equatorial dipole vortices (Rossby solitary waves) is performed. When the amplitude is suffici...
we study the well-posedness of the initial value problem for the chrÄodinger-Boussinesq system. By exploiting the Strichartz estimates for the linear SchrÄodinger operator, we establish the ...
In this paper we construct a completely exponentially fitted finite difference scheme for the initial value problem with small parameter by first and second derivatives. We prove the first order unifo...

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