HIDM2D swMATH ID: 2150 Software Authors: Watanabe, Tsuguhiro Description: HIDM, a general purpose algorithm for nonlinear problems described by partial differential equations A new numerical scheme HIDM (higher-order implicit difference method) is developed to solve comprehensively algebraic equations, ordinary differential equations, partial differential equations and coupled systems of these equations under high accuracy and high numerical stability. High accuracy of the scheme is realized by higher-order discretization method and high numerical stability of the scheme is obtained by implicit difference method and tournament multidivided shooting scheme.par A general purpose computer code HIDM2D is constructed based on the numerical scheme for variety of the time evolution of boundary value problems (1D spatial variable + time). High performance of the code is demonstrated by solving nonlinear dissipative equations, nonlinear dispersive equations, and nonlinear dynamics of unstable systems. Homepage: http://zbmath.org/authors/?q=Watanabe%2C+Tsuguhiro Keywords: nonlinear evolution equations; higher-order implicit difference method; numerical stability; tournament multidivided shooting scheme; nonlinear dissipative equations; nonlinear dispersive equations; nonlinear dynamics; unstable systems Related Software: Cited in: 2 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year HIDM, a general purpose algorithm for nonlinear problems described by partial differential equations. Zbl 0853.65086Watanabe, Tsuguhiro 1993 Cited by 1 Author 2 Watanabe, Tsuguhiro Cited in 1 Serial 1 Annals of Numerical Mathematics Cited in 3 Fields 2 Numerical analysis (65-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) Citations by Year