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MTH-219.4 Computational hyperbolic PDE


Couse Code MTH-219.4
No. of credits 5
Subject Board Mathematics
Course Type Elective course for students in 4th semester of Int-PHd, 3rd year of Int-PhD and PhD
Prerequisites Basic PDE course, knowledge of atleast one of Python/Fortran/C/C++, instructors approval
Class schedule Two classes and one tutorial per week




Linear equations

Conservation laws and differential equations, characteristics and Riemann problem for hyperbolic systems, finite volume methods, high resolution methods, boundary conditions, convergence, accuracy and stability, variable coefficient linear equations.

MUSCL-Hancock, ENO-WENO schemes, time stepping, Central schemes

Nonlinear equations

Scalar problems and finite volume method, nonlinear systems, gas dynamics and Euler equations, FVM for nonlinear systems, approximate Riemann solvers, nonclassical hyperbolic problems, source terms

Multidimensional problems

Some PDE models, fully discrete and semi-discrete methods, methods for scalar and systems of pde

Parallel programming using MPI and PETSc (Fortran/C/C++)


  • Randall J. LeVeque: Finite volume methods for hyperbolic problems, Cambridge Univ. Press.
  • D. I. Ketcheson, R. J. LeVeque and Mauricio J. del Razo, Riemann problems and Jupyter solutions, SIAM.
  • E. F. Toro, Riemann solvers and numerical methods for fluid dynamics, Springer.
  • E. Godlewski and P-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer.