In comparison with traditional methods, the JPI method uses an iterative formula for updating next step approximations and calculating integrals of the shifted Jacobi polynomials are performed via an exact relation. Also, a vector﹎atrix form of the JPI method is provided in details which reduce ...
A subgradient method based dual decomposition distributed algorithm is presented. The algorithm requires the objective function to be convex. But traditional subgradient methods suffer from step curse and require that the objective function is strict convex. Different from subgradient approaches, some new ...
Variational iteration methodConvergence theoremOptimal convergence control parameterPurpose – In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational iteration formula in an aim to ...
In He (1999a) improved Inokuti et al’s method for solving the nonlinear FDE, and proposed the following iterative scheme: (1.60)yapp(x0)=y0(x0)+∫0x0λ(Ly0+Ny0)dx, where λ is the Lagrange multiplier. This formula is called the corrected functional; the second term on the right ...
Various kinds of analytical methods and numerical methods 2–10 were used to solve integral equations. To illustrate the basic idea of the method, we consider the general 2 nonlinear system: Fixed Point Theory and Applications Lut Nut gt, 1.2 where L is a linear operator, N is a nonlinear ...
79 In 1674 a method depending on a new principle, the principle of iteration, was communicated in a letter from Gregory to Collins.1941Phil. Mag. XXXII. 374 After a few iterations the values of er much less than unity will hardly affect the results.1960G. N. Lance Numerical Methods for...
Homework Statement Most functions can be rearranged in several ways to give x = g(x) with which to begin the fixed-point iteration method. For f(x) = e^x − 2x^2 , one g(x) is x = +- sqrt(e^x/2) a) Using the convergence criteria, show that this converges to the root ne...
(14). Numerical example shows that new method leads to the same Laplace transform of the solution aj(t), as that obtained by applying the Laplace transform to the differential Eq. (14), [16]. (3) In this new algorithm is avoided the definition of initial approximation, aj, 0(t), ...
Book 2000, Numerical Methods in ElectromagnetismM.V.K. Chari, S.J. Salon Chapter SOLUTION OF EQUATIONS 11.8.7 Aitken's δ2 Method (Arbitrary Order) This procedure is usually presented as a means for accelerating the convergence of the ordinary functional iteration method, described earlier. If ...
65a,25 – 33 (2010); received November 24, 2008 / revised February 8, 2009In this article, two powerful analytical methods called the variational iteration method (VIM) andthe variational homotopy perturbation method (VHPM) are introduced to obtain the exact and thenumerical solutions of the (...