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Partial Differential Equations (Mathematical Physics Equations)

• Polyanin, A. D., Schiesser, W. E., and Zhurov, A. I, Partial differential equations (2008), Scholarpedia, 3(10):4605.
  • First-Order Partial Differential Equations
  • Second-Order Partial Differential Equations
  • Higher-Order Partial Differential Equations
  • Numerical Methods
• Kudryashov N. A., Seven common errors in finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulation, 2009
• Lectures on Linear Partial Differential Equations (MIT OpenCourseWare) by M.J. Hancock
• Lectures on Solution Methods for Nonlinear Mathematical Physics Equations by A.D. Polyanin
  • Method of Generalized Separation of Variables
  • Method of Functional Separation of Variables
  • Differential Constraints Method
• Method of Lines (numerical solution of partial differential equations) by S. Hamdi, W.E. Schiesser, and G.W. Griffiths
• Maple and Standing Waves by I. Shingareva and C. Lizárraga Celaya, 2006.

Methods for Solving Nonlinear Equations of Mathematical Physics. Selected sections of the textbook by A.D. Polyanin, V.F. Zaitsev and A.I. Zhurov (Fizmatlit, Moscow, 2005 – in Russian):

• Transformations of mathematical physics equations
• Traveling-wave and self-similar solutions. Similarity method
• Method of generalized separation of variables
• Method of functional separation of variables
• Classical method for symmetry reductions of mathematical physics equations
• Differential constraints method for mathematical physics equations
• References