Results 231 to 240 of about 12,171,095 (269)
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Fourth Order Differential Equations
2004In addition to discussing general fourth order nonlinear equations with quasiderivatives, we consider sublinear equations in self-adjoint form, a two term nonlinear equation, and then fourth order linear equations.
Miroslav Bartušek +2 more
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The Sinc-Galerkin Method for Fourth-Order Differential Equations
SIAM Journal on Numerical Analysis, 1991The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $O(e^{ - \kappa \sqrt M } )$ is carefully developed and the special features of the discrete system are described. Spectral properties and conditioning of the associated matrices are
Ralph Conover Smith, John Lund
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The generalized differential quadrature rule for fourth‐order differential equations
International Journal for Numerical Methods in Engineering, 2001AbstractThe generalized differential quadrature rule (GDQR) proposed here is aimed at solving high‐order differential equations. The improved approach is completely exempted from the use of the existing δ‐point technique by applying multiple conditions in a rigorous manner.
Wu, T.Y., Liu, G.R.
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On the stability of a nonhomogeneous vector differential equation of the fourth-order
Applied Mathematics and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Orthogonal polynomials satisfying fourth order differential equations
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981Synopsis These polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends.
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Conjugate Points for Fourth Order Linear Differential Equations
SIAM Journal on Applied Mathematics, 1972Let $r_{i_1 \,i_2 \cdots i_k } = \infty $ mean that no nontrivial solution of $y^{( n )} + \sum\nolimits_{i = 0}^{n - 1} {p_i } ( x )y^{( i )} = 0$ has an $i_1 - i_2 - \cdots - i_k $ distribution of zeros. The main result is the following theorem. THEOREM 1. If$n = 4$and$r_{121} = \infty $, then$r_{31} = r_{31} = \infty $and$\eta _k (
Ridenhour, Jerry R., Sherman, Thomas L.
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A class of fourth order differential equations
Annali di Matematica Pura ed Applicata, 1970The multiplicity of zeros of solutions of the differential equation $$y^{\left( n \right)} \left( x \right) + p\left( x \right)y\left( x \right) = 0$$ are investigated. On account of the results obtained, a class of fourth order differential equations is defined and the properties of the zeros of the solutions, which vanish in x=a, of a subclass,
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Fourth order linear differential equations with imprimitive group
Proceedings of the 2003 international symposium on Symbolic and algebraic computation, 2003In this paper we study fourth order linear differential equations whose differential Galois groups are imprimitive. We derive optimal bounds for the degree of the minimal polynomial of the logarithmic derivative of a Liouvillian solution. This is the lowest possible order where imprimitive non monomial groups occur.
Delphine Boucher +2 more
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Asymptotic Theory for a General Fourth ‐ Order Differential Equation
Mathematische Nachrichten, 1999AbstractAn asymptotic theory is developed for a general fourth‐order differential equation. The theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.
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ON A FOURTH ORDER SYMMETRIC DIFFERENTIAL EQUATION
The Quarterly Journal of Mathematics, 1982Paris, R. B., Wood, A. D.
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