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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

By (author) Xinyuan Wu, By (author) Bin Wang

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The main theme of thisÂ bookÂ is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes theÂ latestÂ advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods,Â andÂ symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in theÂ contextÂ of structure preservation. All the new methods introduced in this bookÂ are provenÂ to be highlyÂ effective compared with the well-known codes in the scientific literature. ThisÂ bookÂ also addressesÂ challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

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