Related papers: Analytical solutions of the Arrhenius-Semenov prob…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical…
We obtain analytical approximate black hole solutions for higher derivative gravity in the presence of Maxwell electromagnetic source. We construct near horizon and asymptotic solutions and then use these to obtain an approximate analytic…
We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier results. Among other things,…
In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution to this equation was obtained. Using the explicit form of…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
This paper investigates a system of nonlinear reaction-diffusion equations modeling the industrial synthesis of ammonia. By applying Lie group analysis, we construct self-similar solutions and derive a reduced system of ordinary…
We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the…
Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible bound\-ary-initial data are generated, The method involves combining the computational solution of a classical…
We compute the full contribution of flavor and (or) Lorentz anomalies to the thermodynamic partition function. Apart from the Wess-Zumino consistency condition the Euclidean generating function must satisfy an extra requirement which we…
The Schwinger-Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the indepedent solutions which respectively…
The article is devoted to the construction of examples that illustrate (using computer calculations) the rate of convergence of Chernoff approximations to the solution of the Cauchy problem for the heat equation. We are interested in the…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…
In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the…