Transcription of Numerical Methods for Partial Differential Equations
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Numerical Methods for Partial Differential Equations
Numerical Methods for PartialDifferential EquationsSeongjai KimDepartment of Mathematics and StatisticsMississippi State UniversityMississippi State, MS 39762 USAE mail: 12, 2021 Seongjai Kim, Department of Mathematics and Statistics, Mississippi StateUniversity, Mississippi State, MS 39762-5921 USA Email: work of the author is supported in part by NSF grant the area of Numerical Methods for Differential Equations ", it seems veryhard to find a textbook incorporating mathematical, physical, and engineer-ing issues of Numerical Methods in a synergistic fashion. So the first goal ofthis lecture note is to provide students a convenient textbook that addressesboth physical and mathematical aspects of Numerical Methods for Partial dif-ferential Equations (PDEs).
N = bgbe a partition of the interval [a;b]. Then, the Lagrange form of interpolating polynomial is formulated as a linear combination of the so-called cardinal functions: p N(x) = XN i=0 L N;i(x)u(x i): (1.3) Here the cardinal functions are defined as L N;i(x) = YN j = 0 j 6= i x x j x i x j 2P N; (1.4) where P N is the set of polynomials of ...
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