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This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…
Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which…
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
Treating diffusion and advection/reaction separately is an effective strategy for solving semilinear advection-diffusion-reaction equations. However, such an approach is prone to suffer from order reduction, especially in the presence of…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of…
The thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to…
In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations (ODEs). Under the specific form of the principal term of…
We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the…
A method for computing minimum ignition energies for gaseous fuel mixtures with detailed and reduced chemistry, by numerical integration of time-dependent conservation equations in a spherically symmetrical configuration, is presented and…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\ge0$ at mesh faces. The method hinges on local discrete reconstruction operators…
We present general series solutions to the Tolman-Oppenheimer-Volkoff equations for compact stellar objects. We develop an algorithm to compute the coefficients of the power series in terms of the equation of state and its derivatives with…
This paper presents a mathematically exact self-similar solution to the joint nonsteady problems of vapour diffusion towards a droplet growing in a vapour-gas medium and of removal of heat released by a droplet into a vapour-gas medium…
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…