Fractional calculus with applications for nuclear reactor dynamics. (2015)

• Record Type: Book
• Further Information: Note: Santanu Saha Ray.
• Authors: Ray, S (Santanu)
• Contents: Mathematical Methods in Nuclear Reactor Physics; Analytical Methods and Numerical Techniques for Solving Deterministic Neutron Diffusion and Kinetic Models; Numerical Methods for Solving Stochastic Point Kinetic Equations; Neutron Diffusion Equation Model in Dynamical Systems ; Introduction; Outline of the Present Study; Application of the Variational Iteration Method to Obtain the Analytical Solution of the NDE; Application of the Modified Decomposition Method to Obtain the Analytical Solution of NDE; Numerical Results and Discussions for Neutron Diffusion Equations; One-Group NDE in Cylindrical and Hemispherical Reactors; Application of the ADM for One-Group Neutron Diffusion Equations; Conclusion; Fractional Order Neutron Point Kinetic Model ; Introduction; Brief Description for Fractional Calculus; FNPKE and Its Derivation; Application of Explicit Finite Difference Scheme for FNPKE; Analysis for Stability of Numerical Computation; Numerical Experiments with Change of Reactivity; Conclusion; Numerical Solution for Deterministic Classical and Fractional Order Neutron Point Kinetic Model ; Introduction; Application of MDTM to Classical Neutron Point Kinetic Equation; Numerical Results and Discussions for Classical Neutron Point Kinetic Model Using Different Reactivity Functions; Mathematical Model for Fractional Neutron Point Kinetic Equation; Fractional Differential Transform Method; Application of MDTM to Fractional Neutron Point Kinetic Equation; Numerical Results and Discussions for Fractional Neutron Point Kinetic Equation; Conclusion; Classical and Fractional Order Stochastic Neutron Point Kinetic Model ; Introduction; Evolution of Stochastic Neutron Point Kinetic Model; Classical Order Stochastic Neutron Point Kinetic Model; Numerical Solution of the Classical Stochastic Neutron Point Kinetic Equation; Numerical Results and Discussions for the Solution of Stochastic Point Kinetic Model; Application of Explicit Finite Difference Method for Solving Fractional Order Stochastic Neutron Point Kinetic Model; Numerical Results and Discussions for the FSNPK Equations; Analysis for Stability of Numerical Computation for the FSNPK Equations; Conclusion; Solution for Nonlinear Classical and Fractional Order Neutron Point Kinetic Model with Newtonian Temperature Feedback Reactivity ; Introduction; Classical Order Nonlinear Neutron Point Kinetic Model; Numerical Solution of Nonlinear Neutron Point Kinetic Equation in the Presence of Reactivity Function; Numerical Results and Discussions for the Classical Order Nonlinear Neutron Point Kinetic Equation; Mathematical Model for Nonlinear Fractional Neutron Point Kinetic Equation; Application of EFDM for Solving the Fractional Order Nonlinear Neutron Point Kinetic Model; Numerical Results and Discussions for Fractional Nonlinear Neutron Point Kinetic Equation with Temperature Feedback Reactivity Function; Computational Error Analysis for the Fractional Order Nonlinear Neutron Point Kinetic Equation; Conclusion; Numerical Simulation Using Haar Wavelet Method for Neutron Point Kinetic Equation Involving Imposed Reactivity Function ; Introduction; Haar Wavelets; Function Approximation and Operational Matrix of the General Order Integration; Application of the HWOM for Solving Neutron Point Kinetic Equation; Numerical Results and Discussions; Convergence Analysis and Error Estimation; Conclusion; Numerical Solution Using Two- Dimensional Haar Wavelet Method for Stationary Neutron Transport Equation in Homogeneous Isotropic Medium ; Introduction; Formulation of Neutron Transport Equation Model; Mathematical Model of the Stationary Neutron Transport Equation in a Homogeneous Isotropic Medium; Application of the Two-Dimensional Haar Wavelet Collocation Method to Solve the Stationary Neutron Transport Equation; Numerical Results and Discussions for Stationary Integer Order Neutron Transport Equation; Mathematical Model for Fractional Order Stationary Neutron Transport Equation; Application of the Two-Dimensional Haar Wavelet Collocation Method to the Fractional Order Stationary Neutron Transport Equation; Numerical Results and Discussions for Fractional Order Neutron Transport Equation; Convergence Analysis of the Two-Dimensional Haar Wavelet Method; Conclusion; References
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 621.4830151583; Nuclear reactors -- Mathematical models; Fractional calculus
• Languages: English
• ISBNs: 9781498727280
• Related ISBNs: 9781498727273
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.