Methods of Solving Differential Equations
Keywords:
PDE, ODE, Separation of Variables, Method of Characteristics, Transform Methods, FDM, FEMAbstract
A variety of physical processes, including heat conduction, wave propagation, fluid movement, and quantum physics, are fundamentally described by partial differential equations, or PDEs. Multiple variable functions and their partial derivatives are involved in these equations. Based on the number of independent variables, the type of boundary and initial conditions, and the nature of the equations (linear or nonlinear), PDEs can be categorized.
References
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Lawrence C. Evans, Partial Differential Equations, American Mathematical Society, 2010.
Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications, 1987.
Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007.
Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, McGraw-Hill Education, 2015.
Daryl L. Logan, A First Course in the Finite Element Method, Cengage Learning, 2016.
Kuchkorov E.I, Jumaeva S.F, A one-dimensional fractional diffusion equation with discontinuous diffusion coefficient, Mathematics, Mechanics and Intellectual Technologies Tashkent, 2023.
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