In this paper, we use the phase plane method for finding finite travelling waves solutions for the diffusion-absorption-convection equation ut = A(|ux|ux)x + B(u)x − Cu , (x, t) ∈ R× R. We show that the existence of solutions which depends on the parameters p, q and n. Also we study the asymptotic behavior of these solutions.

In this paper a singularly perturbed convection–diffusion equation with a discontinuous source term is examined. Boundary and weak interior layers appear in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

By using the Fourier transform method and composite Simpson's integration formula, a symbolically computable approximate solution of an initial value problem for the time dependent convection-diffusion equation is constructed. Given an admissible error e and a point (s,t), the approximation constructed with error less than E at (2, t) can be symbolically obtained using Mathematics 4.0.

A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.

In this presentation the hydro dynamical condition of quorum sensing in the biofilm growth is investigated using convection diffusion reaction equation and analyzed environmental condition. It is used to analyze the influence of hydrodynamics and structural heterogeneities on mass transfer in this quorum sensing mechanism. The future direction of stochastic model of quorum sensing in bacteria i...

In this paper, we present an integral form of convection-diffusion equation. Then a class of alternating group explicit finite difference method (AGE) is constructed based on several asymmetric schemes. The AGE method is unconditionally stable and has the property of parallelism. Results of numerical examples show the AGE method is of high accuracy.

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values. PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

We consider the solution of the convection-diffusion equation in two dimensions by a compact highorder 9-point discretization formula combined with multigrid algorithm. We prove the -asymptotic stability of the coarse-grid operators. Two strategies are examined. A method to compute the asymptotic convergence is described and applied to the multigrid algorithm.

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...