Algorithm 986 swMATH ID: 22693 Software Authors: Mani Mehra; Kuldip Singh Patel Description: Algorithm 986: A Suite of Compact Finite Difference Schemes. A collection of Matlab routines that compute derivative approximations of arbitrary functions using high-order compact finite difference schemes is presented. Tenth-order accurate compact finite difference schemes for first and second derivative approximations and sixth-order accurate compact finite difference schemes for third and fourth derivative approximations are discussed for the functions with periodic boundary conditions. Fourier analysis of compact finite difference schemes is explained, and it is observed that compact finite difference schemes have better resolution characteristics when compared to classical finite difference schemes. Compact finite difference schemes for the functions with Dirichlet and Neumann boundary conditions are also discussed. Moreover, compact finite difference schemes for partial derivative approximations of functions in two variables are also given. For each case a Matlab routine is provided to compute the differentiation matrix and results are validated using the test functions. Homepage: https://dl.acm.org/citation.cfm?id=3119905 Dependencies: Matlab Keywords: Compact finite difference schemes; numerical differentiation; Taylor series expansion; Fourier analysis; PDE; Matlab; TOMS_publication Related Software: Matlab; LTFAT; Algorithm 929 Cited in: 6 Publications Standard Articles 1 Publication describing the Software Year all top 5 Cited by 8 Authors 4 Mehra, Mani 3 Patel, Kuldip Singh 1 Goyal, Kavita 1 Qiao, Leijie 1 Qiu, Wenlin 1 Sharma, Deepika 1 Shukla, Ankita 1 Xu, Da all top 5 Cited in 6 Serials 1 ACM Transactions on Mathematical Software 1 Journal of Computational and Applied Mathematics 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 International Journal of Theoretical and Applied Finance 1 Inverse Problems in Science and Engineering all top 5 Cited in 6 Fields 6 Numerical analysis (65-XX) 3 Partial differential equations (35-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Real functions (26-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year