Transform Methods for Solving Partial Differential Equations

By D. Duffy. 2004

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Clean two‐ and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers (2006, methodology): “r(2) hþ a @ h @z 1⁄4 c @ h @t ; c 1⁄4 a qs qr ð Þ ks ð14Þ Equation (14) is now a linear PDE, which allows the solution of many types of problems using transform methods [Duffy, 1994].”
A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third-Order Differential Equation (2013, unknown): “The Laplace transform has been intensively used to solve nonlinear and linear equations [1–7].”
On Double Sumudu Transform and Double Laplace Transform (2010, methodology): “It is also known that there are two types of these equations; The homogenous equation with constant coefficients has many classical solutions such as separation of variables (Lamb,1995), the methods of characteristics (Myint, 1980 and Constanda, 2002), single Laplace transform and Fourier transform ”
THE NEW INTEGRAL TRANSFORM ELZAKI TRANSFORM (2011, background): “The initial conditions are ( ) ( ) 0 , 0 dy y a b dx = = (6)”
Boundary Control of PDEs (2008, methodology): “Transform methods for PDEs are studied extensively in [49].”