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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)
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)
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