Advanced Numerical Methods in Applied Sciences

doi:10.3390/books978-3-03897-667-7

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Keywords

time fractional differential equations; mixed-index problems; analytical solution; asymptotic stability; conservative problems; Hamiltonian problems; energy-conserving methods; Poisson problems; Hamiltonian Boundary Value Methods; HBVMs; line integral methods; constrained Hamiltonian problems; Hamiltonian PDEs; highly oscillatory problems; boundary element method; finite difference method; floating strike Asian options; continuous geometric average; barrier options; isogeometric analysis; adaptive methods; hierarchical splines; THB-splines; local refinement; linear systems; preconditioners; Cholesky factorization; limited memory; Volterra integral equations; Volterra integro–differential equations; collocation methods; multistep methods; convergence; B-spline; optimal basis; fractional derivative; Galerkin method; collocation method; spectral (eigenvalue) and singular value distributions; generalized locally Toeplitz sequences; discretization of systems of differential equations; higher-order finite element methods; discontinuous Galerkin methods; finite difference methods; isogeometric analysis; B-splines; curl–curl operator; time harmonic Maxwell’s equations and magnetostatic problems; low rank completion; matrix ODEs; gradient system; ordinary differential equations; Runge–Kutta; tree; stump; order; elementary differential; edge-histogram; edge-preserving smoothing; histogram specification; initial value problems; one-step methods; Hermite–Obreshkov methods; symplecticity; B-splines; BS methods; hyperbolic partial differential equations; high order discontinuous Galerkin finite element schemes; shock waves and discontinuities; vectorization and parallelization; high performance computing; generalized Schur algorithm; null-space; displacement rank; structured matrices; stochastic differential equations; stochastic multistep methods; stochastic Volterra integral equations; mean-square stability; asymptotic stability; numerical analysis; numerical methods; scientific computing; initial value problems; one-step methods; Hermite–Obreshkov methods; symplecticity; B-splines; BS methods

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Advanced Numerical Methods in Applied Sciences

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June 2019

306 pages

ISBN978-3-03897-666-0 (Paperback)
ISBN978-3-03897-667-7 (PDF)

https://doi.org/10.3390/books978-3-03897-667-7

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This is a Reprint of the Special Issue Advanced Numerical Methods in Applied Sciences that was published in

Computer Science & Mathematics

Physical Sciences

Summary

The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

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