Computational Mathematics and Applications

Preface
Contents
About the Authors
Analysing Differential Equations with Uncertainties via the Liouville-Gibbs Theorem: Theory and Applications
	1 Introduction and Preliminaries
	2 The 1-P.D.F. of a Random System and the Liouville-Gibbs Equation
		2.1 The Liouville-Gibbs Partial Differential Equation
		2.2 Solving the Liouville-Gibbs Equation
	3 Applications
		3.1 The Random Linear Oscillator
		3.2 The Random Damped Linear Oscillator
		3.3 The Random Logistic Model
	4 Conclusions
	References
Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method
	1 Introduction
	2 Preliminaries
	3 Modified Finite-Difference Method
	4 Stability Analysis
	5 Numerical Experiments
	6 Conclusion
	References
On Modification of an Adaptive Stochastic Mirror Descent Algorithm for Convex Optimization Problems with Functional Constraints
	1 Introduction
	2 Problem Statement and Standard Mirror Descent Basics
	3 Adaptive Stochastic Mirror Descent Algorithm
	4 The Modification of an Adaptive Stochastic Mirror Descent Algorithm
	5 Numerical Experiments
		5.1 Additional Experiments: Fermat-Torricelli-Steiner Problem
	6 Conclusions
	References
Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems
	1 Introduction
	2 Preambles
	3 Pseudo-Euclidean Jordan Triple Systems
		3.1 T*-Extension of Jordan Triple Systems
		3.2 Tits-Kantor-Koecher of Pseudo-Euclidean Jordan Triple Systems
	4 Quadratic Lie Triple Systems
		4.1 Inductive Description of Quadratic Solvable Lie Triple Systems
		4.2 Inductive Description of Quadratic Lie Triple Systems
	5 Conclusion
	References
Comparative Study of Some Numerical Methods for the Standard FitzHugh-Nagumo Equation
	1 Introduction
	2 Organisation of the Paper
	3 Numerical Experiment
	4 Construction of Numerical Scheme from Exact Solution
	5 Scheme of Namjoo and Zibaei
		5.1 Explicit Scheme
		5.2 Implicit Scheme
	6 Nonstandard Finite Difference Scheme (NSFD)
		6.1 NSFD1 Scheme
		6.2 NSFD2 Scheme
		6.3 NSFD3 Scheme
	7 Conclusion
	References
Analytical Solution of Neutron Diffusion Equation in Reflected Reactors Using Modified Differential Transform Method
	1 Introduction
	2 Description of the Method
	3 Theory
		3.1 Reflected Slab Reactor
		3.2 Reflected Spherical Reactor
	4 Results and Comparison
		4.1 Reflected Slab Reactor
		4.2 Reflected Spherical Reactor
	5 Conclusions
	References
Second-Order Perturbed State-Dependent Sweeping Process  with Subsmooth Sets
	1 Introduction
	2 Notations and Preliminaries
	3 Main Result
	4 Delayed Sweeping Process
	5 Examples
	6 Conclusion
	References
Membrane Hydrogen Mixture Separation: Modelling and Analysis
	1 Introduction
	2 Design of Experimental Facility for Membrane Gas Separation on the Base of Nickel Membranes
	3 Simulation of Facility for Membrane Separation
		3.1 Storaging Regime
		3.2 Running Regime
		3.3 Software Package ``Membrane Gas Separation 1.0'' (MGS V. 1.00)
		3.4 Verification
	4 Results and Discussion
	5 Conclusions
	References
An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimisation
	1 Introduction
	2 New Hybrid CGM
	3 Global Convergence Properties
	4 Numerical Result and Discussion
	5 Conclusion
	References
On the Polynomial Decay of the Wave Equation with Wentzell Conditions
	1 Introduction
	2 The Problem
	3 Exponential Stability of a One-Dimensional Problem
	4 Polynomial Stability
	5 Conclusion
	References
Solutions of Fractional Verhulst Model by Modified Analytical and Numerical Approaches
	1 Introduction
	2 Preliminaries of Fractional Calculus
	3 Description of FRPS, RKHS and SS Approaches
		3.1 The Reproducing Kernel Hilbert Space Method
		3.2 The Fractional Residual Power Series Method
		3.3 The Successive Substitutions Technique
	4 Numerical Applications
	5 Conclusion
	References
Is It Worthwhile Considering Orthogonality in Generalised Polynomial Chaos Expansions Applied to Solving Stochastic Models?
	1 Introduction and Motivation
	2 Preliminaries on gPC and Canonical Polynomial Expansions
	3 Comparing gPC and Canonical Polynomial Expansions
	4 Numerical Experiments
	5 Conclusions and Suggestions
	References