A modification of the Haar wavelet method, for which the stepsize of the argument is variable, is proposed. To establish the efficiency of the method three test problems, for which exact solution is known, are considered. Computer simulations show clear preference of the suggested method compared with the Haar wavelet method of a constant stepsize. 2007 Elsevier Inc. All rights reserved.

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

Energy-Based Error Control Strategies Suitable for Long MD Simulations Kante Easley Master of Science Graduate Department of Computer Science University of Toronto 2009 When evaluating integration schemes used in molecular dynamics (MD) simulations, energy conservation is often cited as the primary criterion by which the integrators should be compared. As a result variable stepsize Runge-Kutta ...

Multiple time stepping can be applied to the leapfrog/Stt ormer/Verlet integrator so as to eeect variable stepsize. The strategy maintains the symplecticness, time-reversibility, and second-order accuracy of leapfrog. This method can be applied to pairwise interactions by partitioning them into distance classes and smoothly decomposing the potential energy into the sum of potential energy funct...

The most widely used algorithm for training multiplayer feedforward networks, Error BackPropagation (EBP), is an iterative gradient descend algorithm by nature. Variable stepsize is the key to fast convergence of BP networks. A new optimal stepsize algorithm is proposed for accelerating the training process. It modifies the objective function to reduce the computational complexity of the Jacobi...

Two-step W-methods are linearly implicit time-stepping methods using s external stages that may be processed in parallel. Methods with order s + 1 and stage order s exist. Appropriate generalizations for the concepts of A-and L-stability are derived as well as necessary conditions for A-stability and suucient conditions for stii accuracy. We construct methods of order four where no order reduct...