Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Web-based Simultaneous Equation Solver

* This work has been supported by NIMP, University of Plovdiv under contract No MU-1.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup

Mathematics Subject Classification: 42B35, 35L35, 35K35

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Mathematics Subject Classification: 44A40, 45B05

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05