Fractional calculus with applications for nuclear reactor dynamics

Content: 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