دانلود کتاب Computational Mathematics and Applications

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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