Daisuke Furihata

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A method, called “the discrete variational method”, has been recently presented by Furihata and Matsuo for designing finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations (PDEs). In this paper the method is enhanced so that the derived schemes be highly accurate in space by(More)
We propose two general finite difference schemes that inherit energy conservation property from nonlinear wave equations, such as the nonlinear Klein– Gordon equation (NLKGE). One of proposed schemes is implicit and another is explicit. Many studies exist on FDSs that inherit energy conservation property from NLKGE and we can derive all of their schemes(More)
The asymptotic behavior of continuous dissipative systems and dissipative numerical integrators with fixed time-stepping can be fully investigated by Lyapunov-type theorem on continuous and discrete dynamical systems, respectively. However, once adaptive time-stepping is involved, such theories cease to work, and usually the dynamics should be investigated(More)
s at ICCAM 2012 Multi-Step Skipping Methods with Modified Search Direction for Unconstrained Optimization Nudrat Aamir Department of Mathematical Sciences, University of Essex Wivenhoe Park, Colchester, Essex, CO4 3SQ United Kingdom naamir@essex.ac.uk Joint work with: John A. Ford When dealing with unconstrained non-linear optimization problems using(More)
We consider the discrete gradient method for dissipative linear-gradient systems, which strictly replicates the dissipation property, yielding a remarkable stability. However, it also replicates the nonlinearity of an original equation. To overcome this, we can employ multistep linearly implicit schemes as a relaxation; however, it can in turn destroy the(More)
Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a(More)
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