Showing papers in "Applied Mathematics and Computation in 2005"

TL;DR: It is shown that the so-called ''homotopy perturbation method'' is only a special case of the homotopy analysis method, which contains the auxiliary parameter @?

TL;DR: A framework to determine exact solutions of Bratu-type equations rests mainly on the Adomian decomposition method and is illustrated by studying two boundary value problems and an initial value problem of Bratus-type.

TL;DR: The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the differential transform method.

TL;DR: This paper reduces a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure using the concept of membership function of fuzzy set theory to represent the satisfaction level for both criteria.

TL;DR: The solution obtained by the decomposition method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method.

TL;DR: The tanh method is used for traveling wave solutions of the sine-Gordon and the sinh-Gordon equations and several exact solutions of distinct physical structures are obtained.

TL;DR: A reliable algorithm to determine new exact and new approximate solutions of the generalized Emden-Fowler equation based on Adomian decomposition method with an alternative framework designed to overcome the difficulty of the singular point at x=0.

TL;DR: A new method based on SVD perturbation to deal with the `one example image' problem and two generalized eigenface algorithms are proposed that are more accurate and use far fewer eigenfaces than both the standard eigen face algorithm and the (PC)^2A algorithm.

TL;DR: The Gauss-Sidel iterative method in Allahviranloo for solving Fuzzy system of linear equations (FSLE) is transformed to the successive over relaxation (SOR) method.

TL;DR: It is obtained that the spherical images are spherical helices and it is shown that a curve of constant precession is a slant helix.

TL;DR: It has been shown that the Adomian decomposition method is equivalent to the Jacobi iterative method for FSLE and the algorithm is illustrated by solving some numerical examples.

TL;DR: This paper generalizes a Lipovan’s result of Gronwall-like inequalities to a new type of retarded inequalities which includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals.

TL;DR: The results have demonstrated that the extended Kuhn-Tucker approach can solve a wider class of linear BLP problems can than current capabilities permit.

TL;DR: An attempt has been made to obtain the solution of Bagley–Torvik equation by the relatively new Adomian decomposition method and a good agreement of the results is observed.

TL;DR: The analysis rests mainly on the standard tanh method on the case where the parameter M is noninteger, and a variety of exact travelling wave solutions of distinct physical structures are formally derived.

TL;DR: Adomian decomposition method is used to solve systems of nonlinear fractional differential equations and a linear multi-term fractionaldifferential equation by reducing it to a system of fractional equations each of order at most unity.

TL;DR: The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-cosine method to formally derive a number of travelling wave solutions.

TL;DR: The Adomian decomposition method is used to obtain analytic and approximate solutions of the space-and time-fractional telegraph equations and reveals that it is very effective and convenient.

TL;DR: Detailed numerical results including higher dimensions show that the split-step finite difference method provides accurate and stable solutions for nonlinear Schrodinger equations.

TL;DR: In this paper, the main aim is to develop a method for solving a mxn fuzzy linear system for m= by solving the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.

TL;DR: In this article, the authors presented a numerical study of the flow of an electrically conducting power-law fluid in the presence of a uniform transverse magnetic field, governed by the nonlinear differential equationn(-f^'')^(^n^-^1^)f^@?-(f^')^2+2nn+1ff^''-Mf^'=0.

TL;DR: An eigenvector method-based nonlinear programming (NLP) approach is developed to generate interval weights that can meet pre-determined consistency requirements and a simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives.

TL;DR: Numerical solutions of the one-dimensional Burgers' equation are obtained by a method based on collocation of cubic B-splines over finite elements which yields a system of difference equation which is shown to be unconditionally stable.

TL;DR: This research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS, and the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.

TL;DR: The linear, speed, nonlinear doubly-periodic function and nonlinear hyperbolic function feedback controls are used to suppress hyperchaos to unstable equilibrium and the Routh-Hurwitz theorem is used to derive the conditions of stability of controlled hyperchaotic Chen systems.

TL;DR: Several numerical solution are obtained using a Runge-Kutta algorithm for high-order initial value problems for 1 ⩽ a ⦽ 2 and a = 2 for flat-plate flow in fluid mechanics.

TL;DR: A new multi-secret sharing scheme based on two variable one-way function and Hermite interpolating polynomial is presented, in which the participants' shadows remain secret and can be reused.

TL;DR: Adomian method is used to find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equation of the second kind.

TL;DR: This paper revisits the use of the Taylor series method for the numerical integration of ODEs and DAEs using an efficient variable-step variable-order scheme.

TL;DR: With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of neutral Lotka-Volterra system with periodic delays and feedback control.