[PDF] Top 20 Numerical continuation methods for nonlinear equations and bifurcation problems

... derive methods which have the same stability properties, close to x* , as the methods derived in Chapters 2 and 3, for solving ...the methods of sections ...some numerical tests carried out ... See full document

... of nonlinear boundary value problems for ordinary differential equations side by side with numerical methods, it is often used an appropriate technique based upon some types of ... See full document

... iterative methods used for the solution of linear systems (like Gauss–Seidel, SOR, Jacobi, and others) to the solution of systems of nonlinear algebraic and/or transcendental equations, as well as to ... See full document

... R., ''Some Numerical Results for the Solution of the Heat Equation Backwards in Time," Numerical Solutions of Nonlinear Differential Equations.. and Hilbert D., Methods of Mathematical P[r] ... See full document

... iterative methods with cubic convergence for solving nonlinear systems are ...Several numerical examples for solving the system of nonlinear equations and boundary-value problems ... See full document

... are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult.. For the easier problems th[r] ... See full document

... elements methods (FEMs) with numerical integration play a central role in nu- merical homogenization methods for partial differential equations with multiple scales, as the effective data in a ... See full document

... and nonlinear mathematical, engineering and physical problems, many of the numerical methods are used for seeking approximate solutions such as Collocation method, Taylor expansion method, ... See full document

... Numerical differentiation, a topic we consider in § 3.1, is a simple matter if the smooth and nonsmooth parts of the nonlinearity are split. Here, we can prove accuracy only if one is differenti- ating in ... See full document

... several numerical methods have been proposed to approximate exact solutions for such ...such methods are the Adomian decomposition method [3,4], collocation spline method [5], Variational iteration ... See full document

... Sobolev equations have important applications in many mathematical and physical problems, such as the percolation theory of the fluid flowing through the cracks [5], the transfer problem of the moisture in ... See full document

... many problems where nonlinear system of equations occurs such as engineering, mechanics, medicine, chemistry, and ...a nonlinear system of equations and here the problem will be solved ... See full document

... several methods to solve nonlinear equations such as Newton’s method, secant method, bisection method and et ...well-known numerical methods for solving linear and nonlinear ... See full document

... The problem of inuencing a uid ow to behave in a desirable fashion has been studied by numerous scientists over the centuries. Due to the complexity of the dynamics of uid, the nature of the application, and the cost of ... See full document

... differential equations and variational problems with nonstandard pr- growth conditions is a new and interesting ...from nonlinear elasticity theory, electrorheological fluids, image processing, and so ... See full document

... The nonlinear equation with jumping nonlinearity has been extensively studied by many authors. For the fourth order elliptic equation, Taratello 3 and Micheletti and Pistoia 4, 5 proved the existence of nontrivial ... See full document

... algebraic equations (IAEs) are mixed system of the first kind and the second kind Volterra integral ...their numerical solution using collocation methods on piecewise polynomial spaces has attracted ... See full document

... The following theorems can be deduced from Equations (13) and (15). Theorem 1 If then y x ( ) = f x ( ) ± g x ( ) , Y k ( ) = F k ( ) ± G k ( ) . Theorem 2 If the y x ( ) = af x ( ) , , n Y k ( ) = aF k ( ) a ∈  ... See full document

... In Section 3 we present and prove the convergence of some numerical schemes for computing the nontrivial solution curves of 1.1 in a neighborhood of a simple bifurcation point 0,0 for gi[r] ... See full document

... Here we will invoke a continuation theorem of Mawhin for obtaining such solutions. More specifically, let X and Y be two Banach spaces and L : Dom L ⊂ X → Y is a linear mapping and N : X → Y a continuous mapping ... See full document