منابع مشابه
A multi-mesh finite element method for Lagrange elements of arbitrary degree
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviors of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational run...
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The problem of investing y (0) dollars at time 0 to duplicate a contingent claim is formulated as a dynamic optimization problem and solved by the Lagrange method. As an example, the well-known formula of Black and Scholes on option pricing is derived. If the function defining dy (t) is concave in y (t), owing to costs of trading in incomplete markets, there is economy of scale in producing man...
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The Lagrange multiplier method of Babuska for the approximate solution of Dirichlet's problem for second order elliptic equations is reformulated. Based on this formulation, new estimates for the error in the solution and the boundary flux are given. Efficient methods for the solution of the approximate problem are discussed.
متن کاملOn the Method of Lagrange Multipliers
and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...
متن کاملLagrange mesh, relativistic flux tube, and rotating string.
The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.
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ژورنال
عنوان ژورنال: Physics Reports
سال: 2015
ISSN: 0370-1573
DOI: 10.1016/j.physrep.2014.11.006