偏微分方程式の数値解法 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "偏微分方程式の数値解法" in Japanese language version.

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17wikipedia.org

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1springer.com

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1doi.org

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doi.org (Global: 2^nd place; Japanese: 6^th place)

Nakao, Mitsuhiro T; Plum, Michael; Watanabe, Yoshitaka (2019). Numerical verification methods and computer-assisted proofs for partial differential equations. Springer. doi:10.1007/978-981-13-7669-6

springer.com (Global: 274^th place; Japanese: 596^th place)

link.springer.com

Nakao, Mitsuhiro T; Plum, Michael; Watanabe, Yoshitaka (2019). Numerical verification methods and computer-assisted proofs for partial differential equations. Springer. doi:10.1007/978-981-13-7669-6

wikipedia.org (Global: low place; Japanese: low place)

en.wikipedia.org

Ablowitz, M. J., & Segur, H. (1981). Solitons and the inverse scattering transform. SIAM.
Hairer, E., Lubich, C., & Wanner, G. (2006). Geometric numerical integration: structure-preserving algorithms for ordinary differential equations. en:Springer Science & Business Media.
Logg, A., Mardal, K. A., & Wells, G. (Eds.). (2012). Automated solution of differential equations by the finite element method: The FEniCS book. en:Springer Science & Business Media.
Feng, B. F., Maruno, K. I., & Ohta, Y. (2010). A self-adaptive moving mesh method for the Camassa–Holm equation. en:Journal of computational and applied mathematics, 235(1), 229-243.
Miyatake, Y., Sogabe, T., & Zhang, S. L. (2018). On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems. en:Journal of Computational and Applied Mathematics, 342, 58-69.
Bramble, J. H., & Hubbard, B. E. (1962). On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation. en:Numerische Mathematik, 4(1), 313-327.
Matsunaga, N., & Yamamoto, T. (2000). Superconvergence of the Shortley–Weller approximation for Dirichlet problems. en:Journal of computational and applied mathematics, 116(2), 263-273.
Swarztrauber, P. N., & Sweet, R. A. (1973). The direct solution of the discrete Poisson equation on a disk. en:SIAM Journal on Numerical Analysis, 10(5), 900-907.
Fox, L., Henrici, P., & Moler, C. (1967). Approximations and bounds for eigenvalues of elliptic operators. en:SIAM Journal on Numerical Analysis, 4(1), 89-102.
Yuan, Q., & He, Z. (2009). Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods. en:Journal of computational and applied mathematics, 233(4), 1083-1090.
Bramble, J. H., & Osborn, J. E. (1973). Rate of convergence estimates for nonselfadjoint eigenvalue approximations. en:Mathematics of computation, 27(123), 525-549.
Boffi, D., Brezzi, F., & Gastaldi, L. (2000). On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form. en:Mathematics of computation, 69(229), 121-140.
Hashemi, B., & Trefethen, L. N. (2017). Chebfun in three dimensions. en:SIAM Journal on Scientific Computing, 39(5), C341-C363.
Wright, G. B., Javed, M., Montanelli, H., & Trefethen, L. N. (2015). Extension of Chebfun to periodic functions. en:SIAM Journal on Scientific Computing, 37(5), C554-C573.
Liu, X., & Oishi, S. (2013). Verified eigenvalue evaluation for the Laplacian over polygonal domains of arbitrary shape. en:SIAM Journal on Numerical Analysis, 51(3), 1634-1654.
Oishi, S. (1995). Numerical verification of existence and inclusion of solutions for nonlinear operator equations. en:Journal of Computational and Applied Mathematics, 60(1-2), 171-185.
Mizuguchi, M., Takayasu, A., Kubo, T., & Oishi, S. I. (2017). A method of verified computations for solutions to semilinear parabolic equations using semigroup theory. en:SIAM Journal on Numerical Analysis, 55(2), 980-1001.