Variational iteration method for solving nonlinear boundary value problems

DOI10.1016/j.amc.2006.05.138zbMath1110.65068OpenAlexW2037775085MaRDI QIDQ865595

Salah Abuasad, Shaher Momani, Zaid M. Odibat

Publication date: 19 February 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.138

zbMATH Keywords

Lagrange multiplierscomparison of methodsnumerical examplesnonlinear boundary value problemsvariational iteration methodTroesch's problemAdomian decomposition

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

Successive complementary expansion method for solving Troesch's problem as a singular perturbation problem, Approximate solutions to nonlinear fractional order partial differential equations arising in ion-acoustic waves, Matrix method based on the second kind Chebyshev polynomials for solving time fractional diffusion-wave equations, A closed-form approximation for the fractional Black-Scholes model with transaction costs, An efficient algorithm for solving Troesch's problem, The method of finding solutions of partial dynamic equations on time scales, On the solutions of three-point boundary value problems using variational-fixed point iteration method, On solving the Troesch problem for large sensitivity parameter values using exact derivative evaluations, Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions, Application of He's variational iteration method for solution of differential-algebraic equations, Unnamed Item, Numerical solution of two-point nonlinear boundary value problems via Legendre-Picard iteration method, A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM, Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations, An efficient technique based on Green's function for solving two-point boundary value problems and its convergence analysis, Numerical solutions of Troesch and Duffing equations by Taylor wavelets, Variational iteration method for elastodynamic Green's functions, An iterative technique for a class of Dirichlet nonlinear BVPs: Troesch's problem, Numerical solution of functional integral equations by the variational iteration method, Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems, Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes, On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equations, Mathematical modeling on the effect of equivalence ratio in emission characteristics of compression ignition engine with hydrogen substitution, An iterative technique for solving a class of local and nonlocal elliptic boundary value problems, Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions, Application of Legendre wavelets for solving fractional differential equations, An efficient approach for solving nonlinear Troesch's and Bratu's problems by wavelet analysis method, Analysis of convective straight and radial fins with temperature-dependent thermal conductivity using variational iteration method with comparison with respect to finite element analysis, A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula, An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method, A geometric approach for solving Troesch's problem, Stochastic numerical treatment for solving Troesch's problem, A generalized differential transform method for linear partial differential equations of fractional order, Effects of nonlinearity on the variational iteration solutions of nonlinear two-point boundary value problems with comparison with respect to finite element analysis, Comparative analysis of power-law fin-type problems using variational iteration method and finite element method, A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations, The approximate solution of steady temperature distribution in a rod: Two-point boundary value problem with higher order nonlinearity, Solving boundary value problems of ordinary differential equations with non-separated boundary conditions, The steady temperature distributions with different types of nonlinearities, A new application of He's variational iteration method for the solution of the one-phase Stefan problem, Exact solution of the heat equation with boundary condition of the fourth kind by He's variational iteration method, Variational iteration method for Sturm-Liouville differential equations, Numerical solution of Troesch's problem by simple shooting method, A variational iteration method for solving Troesch's problem, Comparison between variational iteration method and homotopy perturbation method for linear and nonlinear partial differential equations with the nonhomogeneous initial conditions, Rigorous solution of slopes' stability considering hydrostatic pressure, A new modification of the variational iteration method for Van der Pol equations, Solving two-point boundary value problems using combined homotopy perturbation method and Green's function method, A Multiple Variational Iteration Method for Nonlinear Two-Point Boundary Value Problems with Nonlinear Conditions, Optimization solution of Troesch's and Bratu's problems of ordinary type using novel continuous genetic algorithm, Solving ordinary differential equations using an optimization technique based on training improved artificial neural networks, Analytical solution for a suspension bridge by applying HPM and VIM, An efficient approach for solving second-order nonlinear differential equation with Neumann boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational iteration method for solving Burgers and coupled Burgers equations
• Application of He's variational iteration method to Helmholtz equation
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• On the closed form solution of Troesch's problem
• A simple approach to a sensitive two-point boundary value problem
• Variational iteration method for delay differential equations
• Variational principles for some nonlinear partial differential equations with variable coefficients
• Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method
• Search for variational principles in electrodynamics by Lagrange method
• Application of variational iteration method to nonlinear differential equations of fractional order
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Approximate solution of nonlinear differential equations with convolution product nonlinearities
• An algorithm for solving boundary value problems
• Analytical approach to linear fractional partial differential equations arising in fluid mechanics
• Numerical comparison of methods for solving linear differential equations of fractional order
• An iteration formulation for normalized diode characteristics
• Variational Theory for Linear Magneto-Electro-Elasticity
• An Approximate Solution for One-Dimensional Weakly Nonlinear Oscillations
• Variational iteration method for autonomous ordinary differential systems
• A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems