Numerical Methods for Ordinary Differential Equations

DOI10.1007/978-0-85729-148-6zbMath1209.65070OpenAlexW4247080625MaRDI QIDQ5893967

Publication date: 25 November 2010

Published in: Springer Undergraduate Mathematics Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-85729-148-6

zbMATH Keywords

textbook stochastic differential equations Runge-Kutta methods Taylor method linear multistep methods geometric integration long-term dynamics Euler's method modified equations adaptive step-size selection

Mathematics Subject Classification ID

Related Items (76)

On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D ⋮ Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations ⋮ Impact of force function formulations on the numerical simulation of centre-based models ⋮ Discrete time-variant nonlinear optimization and system solving via integral-type error function and twice ZND formula with noises suppressed ⋮ Recurrent neural dynamics for handling linear equation system with rank-deficient coefficient and disturbance existence ⋮ Energy preserving turbulent simulations at a reduced computational cost ⋮ Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction ⋮ The Williams step increases the stability and accuracy of the hoRA time filter ⋮ Discrete-time ZD, GD and NI for solving nonlinear time-varying equations ⋮ Taylor series expansion using matrices: an implementation in MATLAB{\circledR} ⋮ Time filters increase accuracy of the fully implicit method ⋮ High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation ⋮ Tracking control of ship course system using new six-step zead (Zhang et al discretization) formula with high precision ⋮ A numerical analysis for FRW universe in f(R,T) gravity ⋮ Continuous and discrete zeroing dynamics models using JMP function array and design formula for solving time-varying Sylvester-transpose matrix inequality ⋮ Mathematical modelling for the role of CD\(4^+\)T cells in tumor-immune interactions ⋮ A blended continuous-discontinuous finite element method for solving the multi-fluid plasma model ⋮ Control of pendulum tracking (including swinging up) of IPC system using zeroing-gradient method ⋮ Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs ⋮ Refactorization of the midpoint rule ⋮ Analysis of a Filtered Time-Stepping Finite Element Method for Natural Convection Problems ⋮ Stepsize domain confirmation and optimum of zead formula for future optimization ⋮ Euler scheme for approximation of solution of nonlinear ODEs under inexact information ⋮ Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow ⋮ Unnamed Item ⋮ Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. I: Periodic boundary conditions ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. II: Nonreflecting boundary conditions ⋮ New five-step DTZD algorithm for future nonlinear minimization with quartic steady-state error pattern ⋮ Temporal accuracy of FastRK3 ⋮ The series expansions and blow-up time estimation for the solutions of convolution Volterra-Hammerstein integral equations ⋮ Adaptive step size controllers based on Runge-Kutta and linear-neighbor methods for solving the non-stationary heat conduction equation ⋮ Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation ⋮ Model reduction and implicit-explicit Runge-Kutta schemes for nonlinear stiff initial-value problems ⋮ Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method ⋮ Optimal switching control of 1,3-propanediol fed-batch production with a cost on smooth feeding rate variation ⋮ Derivation of weighting rules for developing a class of A-stable numerical integration scheme: αI-(2 + 3)P method ⋮ On stability of difference schemes. Central schemes for hyperbolic conservation laws with source terms ⋮ Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D ⋮ Note on Weakly and Strongly Stable Linear Multistep Methods ⋮ New zeroing neural dynamics models for diagonalization of symmetric matrix stream ⋮ Unnamed Item ⋮ Asymptotic behavior of solutions of a nonlinear degenerate chemotaxis model ⋮ Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties ⋮ Unnamed Item ⋮ Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed ⋮ Discrete-time zeroing neural network of \(O(\tau^4)\) pattern for online solving time-varying nonlinear optimization problem: application to manipulator motion generation ⋮ Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data ⋮ Unnamed Item ⋮ Explicit-in-time goal-oriented adaptivity ⋮ Design and analysis of two discrete-time ZD algorithms for time-varying nonlinear minimization ⋮ Different-level algorithms for control of robotic systems ⋮ Real-time robot manipulator tracking control as multilayered time-varying problem ⋮ Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves ⋮ Unnamed Item ⋮ Boundary update via resolvent for fluid-structure interaction ⋮ Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization ⋮ New models for solving time-varying LU decomposition by using ZNN method and ZeaD formulas ⋮ Continuous and discrete zeroing neural dynamics handling future unknown-transpose matrix inequality as well as scalar inequality of linear class ⋮ Neural network approach for solving nonsingular multi-linear tensor systems ⋮ Discrete-time Zhang neural networks for time-varying nonlinear optimization ⋮ General six-step discrete-time Zhang neural network for time-varying tensor absolute value equations ⋮ Linear high-order energy-preserving schemes for the nonlinear Schrödinger equation with wave operator using the scalar auxiliary variable approach ⋮ Unnamed Item ⋮ Geometric integrators and the Hamiltonian Monte Carlo method ⋮ Solving advection equations by applying the Crank-Nicolson scheme combined with the Richardson extrapolation ⋮ Variations on a Theme of Euler ⋮ A Variable Stepsize, Variable Order Family of Low Complexity ⋮ Adaptive reachability algorithms for nonlinear systems using abstraction error analysis ⋮ Efficient nonlinear filter stabilization of the Leray-\(\alpha\) model ⋮ Nonlinear problems with blow-up solutions: numerical integration based on differential and nonlocal transformations, and differential constraints ⋮ Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness ⋮ The generalized viscosity explicit rules for solving variational inclusion problems in Banach spaces ⋮ Time-adaptive partitioned method for fluid-structure interaction problems with thick structures ⋮ General 9-instant discrete-time Zhang neural network for time-dependent applications ⋮ Unnamed Item

Uses Software

This page was built for publication: Numerical Methods for Ordinary Differential Equations