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Full Description
Applied Algebraic and Differential Calculus is an edited book consisting of 18 open-access articles on mathematical analysis and computational methodologies for solving differential equations, as well as matrix eigenvalue, boundary value, and bifurcation problems. It includes a variety of algebraic and numerical strategies from decomposition to neural network based methods. Reading this book requires some knowledge in advanced calculus, differential equations, matrix computations. This book is intended to reach an academic audience ranging from graduate student to experienced researchers.
Contents
Chapter 1 The Eight Epochs of Math as Regards Past and Future Matrix Computations
Chapter 2 Solving Second-Order Differential Equations by Decomposition
Chapter 3 Decomposition of Ordinary Differential Equations
Chapter 4 Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform
Chapter 5 Higher Order Haar Wavelet Method for Solving Differential Equations
Chapter 6 Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag-Leffler Functions
Chapter 7 Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems
Chapter 8 Matrix Iteration Algorithms for Solving the Generalized Lyapunov Matrix Equation
Chapter 9 A Brief Summary of the Finite Element Method for Differential Equations
Chapter 10 An Efficient Finite Element Method and Error Analysis for Eigenvalue Problem of Schrödinger Equation with an Inverse Square Potential on Spherical Domain
Chapter 11 Solving Fractional Differential Equations by Using Triangle Neural Network
Chapter 12 A Novel Improved Extreme Learning Machine Algorithm in Solving Ordinary Differential Equations by Legendre Neural Network Methods
Chapter 13 Bifurcation Theory of Dynamical Chaos
Chapter 14 Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation
Chapter 15 Observations on the Computation of Eigenvalue and Eigenvector Jacobians
Chapter 16 A Note on Some Nonlinear Principal Eigenvalue Problems
Chapter 17 Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
Chapter 18 Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations
