Author | Collatz, Lothar. author |
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Title | The Numerical Treatment of Differential Equations [electronic resource] / by Lothar Collatz |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1960 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-88434-4 |
Descript | XV, 568 p. 6 illus., 1 illus. in color. online resource |
I Mathematical preliminaries and some general principles -- Some notes on the numerical examples -- ยง 1. Introduction to problems involving differential equations -- ยง 2. Finite differences and interpolation formulae -- ยง 3. Further useful formulae from analysis -- ยง 4. Some error distribution principles -- ยง 5. Some useful results from functional analysis -- II Initial-value problems in ordinary differential equations -- ยง 1. Introduction -- ยง 2. The Runge-Kutta method for differential equations of the n-th order -- ยง 3. Finite-difference methods for differential equations of the first order -- ยง 4. Theory of the finite-difference methods -- ยง 5. Finite-difference methods for differential equations of higher order -- III Boundary-value problems in ordinary differential equations -- ยง 1. The ordinary finite-difference method -- ยง 2. Refinements of the ordinary finite-difference method -- ยง 3. Some theoretical aspects of the finite-difference methods -- ยง 4. Some general methods -- ยง 5. Ritzโs method for second-order boundary-value problems -- ยง 6. Ritzโs method for boundary-value problems of higher order -- ยง 7. Series solutions -- ยง 8. Some special methods for eigenvalue problems -- IV Initial-and initial-/boundary-value problems in partial differential equations -- The need for a sound theoretical foundation -- ยง 1. The ordinary finite-difference method -- ยง 2. Refinements of the finite-difference method -- ยง 3. Some theoretical aspects of the finite-difference methods -- ยง 4. Partial differential equations of the first order in one dependent variable -- ยง 5. The method of characteristics for systems of two differential equations of the first order -- ยง 6. Supplements -- V Boundary-value problems in partial differential equations -- ยง 1. The ordinary finite-difference method -- ยง 2. Refinements of the finite-difference method -- ยง 3. The boundary-maximum theorem and the bracketing of solutions -- ยง 4. Some general methods -- ยง 5. The Ritz method -- ยง 6. The Trefftz method -- VI Integral and functional equations -- ยง 1. General methods for integral equations -- ยง 2. Some special methods for linear integral equations -- ยง 3. Singular integral equations -- ยง 4. Volterra integral equations -- ยง 5. Functional equations -- Table III. Finite-difference expressions for ordinary differential equations -- Table IV. Euler expressions for functions of one independent variable -- Table V. Euler expressions for functions of two independent variables -- Table VII. Catalogue of examples treated -- Author index