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  • 1
    Electronic Resource
    Electronic Resource
    An approximation theorem for second-order evolution equations (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 127-142 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396311
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 31-53 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65M60 ; CR: G. 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We approximate the solutions of an initial- and boundary-value problem for nonlinear Schrödinger equations (with emphasis on the ‘cubic’ nonlinearity) by two fully discrete finite element schemes based on the standard Galerkin method in space and two implicit. Crank-Nicolson-type second-order accurate temporal discretizations. For both schemes we study the existence and uniqueness of their solutions and proveL 2 error bounds of optimal order of accuracy. For one of the schemes we also analyze one step of Newton's method for solving the nonlinear systems that arise at every time step. We then implement this scheme using an iterative modification of Newton's method that, at each time stept n , requires solving a number of sparse complex linear systems with a matrix that does not change withn. The effect of this ‘inner’ iteration is studied theoretically and numerically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385769
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Some remarks on a class of rational approximations to the cosine (1980)
    Springer
    BIT 20 (1980), S. 204-211 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some previously introduced methods for the numerical solution of second-order evolution equations based on a class of rational approximations to the cosy, y real, with denominators (1+x 2 y 2) s are revisited. It is shown that maximal accuracy occurs for each integers≧1 for a suitable choice of the parameterx. An improved sufficient condition for unconditional stability is obtained. Conditional stability and periodicity of these methods are also studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933192
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On some unconditionally stable, higher order methods for the numerical solution of the structural dynamics equations (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1613-1621 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Third- and fourth-order accurate Nørsett rational approximations to the exponential and associated semi-implicit Runge-Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second-order equations of structural dynamics.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181104
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    Paper (German National Licenses)
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