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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).

ferential equations (PDEs). In solving PDEs numerically, the following are essential to consider: •physical laws governing the differential equations (physical understand-ing), •stability/accuracy analysis of numerical methods (mathematical under-standing), •issues/difficulties in realistic applications, and

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