Numerical Solution of Partial Differential Equations

CSCI-6840

Numerical methods and analysis for linear and nonlinear PDEs with applications from heat conduction, wave propagation, solid and fluid mechanics, and other areas. Basic concepts of stability and convergence (Lax equivalence theorem, CFL condition, energy methods). Methods for parabolic problems (finite differences, method of lines, ADI, operator splitting), methods for hyperbolic problems (vector systems and characteristics, dissipation and dispersion, shocks capturing and tracking schemes), methods for elliptic problems (finite difference and finite volume methods).

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