An approximate analytic solution of the nonlinear Riccati differential equation

DOI10.1016/j.jfranklin.2010.10.005zbMath1210.34016OpenAlexW2058829853WikidataQ115346462 ScholiaQ115346462MaRDI QIDQ621936

Sumit K. Garg

Publication date: 31 January 2011

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2010.10.005

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear ordinary differential equations and systems (34A34)

Related Items (27)

Variational iteration method for fractional calculus -- a universal approach by Laplace transform ⋮ SOLUTION OF RICCATI DIFFERENTIAL EQUATION WITH GREEN’S FUNCTION AND PADÈ APPROXIMATION TECHNIQUE ⋮ Numerical solution of Riccati equations by the Adomian and asymptotic decomposition methods over extended domains ⋮ Numerical approximation of Riccati fractional differential equation in the sense of Caputo-type fractional derivative ⋮ Homotopy perturbation transform method for nonlinear differential equations involving to fractional operator with exponential kernel ⋮ Fixed-term homotopy ⋮ Fractional-order Riccati differential equation: analytical approximation and numerical results ⋮ A decomposition analysis on convecting-radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient ⋮ Application of numerical inverse Laplace transform algorithms in fractional calculus ⋮ Generalized difference simulation for coupled transport models of unsaturated soil water flow and solute ⋮ Application of a parametrization method to problem of optimal control ⋮ Rational biparameter homotopy perturbation method and Laplace-Padé coupled version ⋮ Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense ⋮ Approximations for large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum ⋮ Analytical solution of a nonlinear index-three DAEs system modelling a slider-Crank mechanism ⋮ Analytical solutions of fractional differential equations using the convenient Adomian series ⋮ A convenient Adomian-Pade technique for the nonlinear oscillator equation ⋮ The Laplace-Adomian-Padé technique for the ENSO model ⋮ An improved approximate analytic solution for Riccati equations over extended intervals ⋮ LARGE INTERVAL SOLUTION OF THE EMDEN–FOWLER EQUATION USING A MODIFIED ADOMIAN DECOMPOSITION METHOD WITH AN INTEGRATING FACTOR ⋮ Unnamed Item ⋮ Generalized homotopy method for solving nonlinear differential equations ⋮ Piece-wise-polynomial method ⋮ Application of fuzzy Picard method for solving fuzzy quadratic Riccati and fuzzy Painlevé I equations ⋮ Modified differential transform method for solving the model of pollution for a system of lakes ⋮ A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains ⋮ Modified reduced differential transform method for partial differential-algebraic equations

Cites Work

• Unnamed Item
• Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control
• An efficient method for quadratic Riccati differential equation
• Solution of the Riccati equation by continued fractions
• The simple pendulum and the periodic LQG control problem
• A piecewise variational iteration method for Riccati differential equations
• A new method for determining the solution of Riccati differential equations
• A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials
• Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators
• Synthesis of finite-dimensional Riccati-based feedback controls for problems arising in structural acoustics
• Solving frontier problems of physics: the decomposition method
• A Laplace decomposition algorithm applied to a class of nonlinear differential equations
• A decomposition method for solving the convective longitudinal fins with variable thermal conductivity
• Solving Riccati differential equation using Adomian's decomposition method
• A Riccati equation approach to the robust memoryless stabilization of discrete time-delay systems
• Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method
• Iterated He's homotopy perturbation method for quadratic Riccati differential equation
• Homotopy analysis method for quadratic Riccati differential equation
• Numerical solution of Duffing equation by the Laplace decomposition algorithm

This page was built for publication: An approximate analytic solution of the nonlinear Riccati differential equation