In this paper, a modified iteration method (MIM) has been proposed to solve nonlinear second-order ODEs. Convergence analysis and error estimate of the proposed method are also discussed. Computational efficiency of this method is illustrated through numerical examples....
In an iterative algorithm, mathematical procedures are used for solving a complex problem. In computational complexity problems, this method computes results through nth approximation from the previously used answers. An initial guess and sometimes termination criteria are used to start and stop the prob...
In 1687, Newton proposed the least resistance problem of a rotating body, i.e., to choose an appropriate function of y(x), such that (6.1)J=min∫x1x2y(x)y′2(x)1+y′2(x)ⅆx. The variational method was developed rapidly in the 20th century, mainly owing to the development of...
contrast spatial structurefemtosecond laser pulsefiniteヾifference schemeNeumann problem solvabilitynumerical methodoptical bistabilitydoi:10.1002/cmm4.1092Vyacheslav TrofimovMaria LoginovaVladimir EgorenkovJohn Wiley & Sons, LtdComputational and Mathematical Methods...
Variational iteration methodSpectral collocation methodNonlinear Fredholm integral equationIn this paper, an efficient numerical method which is a combination of the variational iteration method and the spectral collocation method is developed for solving a class of nonlinear Fredholm......
Thereduce()method will reduce an array to a single value. This is seen commonly with numbers, such as finding the sum of all the numbers in an array. letnumbers=[42,23,16,15,4,8];// Get the sum of all numerical valuesletsum=numbers.reduce((a,b)=>{returna+b;});sum; ...
Finally, the method is explained by 2 illustrative examples.ROUHPARVARDepartment of MathematicsHamidDepartment of MathematicsABBASBANDYDepartment of MathematicsSaeidDepartment of MathematicsWalailak Journal of Science & TechnologyRouhparvar, H, Abbasbandy, S: Numerical solution of the uncertain characteristic ...
In this paper, the author proposes a new perturbation technique coupling with iteration method, yielding a powerful mathematical tool for an analytical solution of nonlinear equations. The obtained results are valid not only for weakly nonlinear problems but also for strongly nonlinear ones. Furthermore...
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 ...
He's variational iteration method is applied to solve th order semidifferential equations. Comparison is made between collocation spline method based on L... G Asghar,A Abdolsaeed - 《Mathematical Problems in Engineering》 被引量: 20发表: 2008年 Numerical solutions of time fractional degenerate par...