HAMAD Formulations: General Formulations for Exact and Similarity Transformations of ODEs and PDEs
نویسنده
چکیده
The current paper outlines a new algorithm, which is used to determine the exact solutions of ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (III) Formulations for similarity transformations of PDEs contains three independent variables. By using these formulations enable readers can calculate the similarity transformations which transform PDEs to ODEs and also can calculate exact solutions of ODEs . Some examples are presented.
منابع مشابه
Dufour and Soret Effects on Unsteady Heat and Mass Transfer for Powell-Eyring Fluid Flow over an Expanding Permeable Sheet
In the present analysis, the Dufour and Soret effects on unsteady heat-mass transfer of a viscous incompressible Powell-Eyring fluids flow past an expanding/shrinking permeable sheet are reported. The fluid boundary layer develops over the variable sheet with suction/injection to the non-uniform free stream velocity. Under the symmetry group of transformations, the governing equations along wit...
متن کاملPossessions of viscous dissipation on radiative MHD heat and mass transfer flow of a micropolar fluid over a porous stretching sheet with chemical reaction
This article presents the heat and mass transfer characteristics of unsteady MHD flow of a viscous, incompressible and electrically conducting micropolar fluid in the presence of viscous dissipation and radiation over a porous stretching sheet with chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) by applying suitable si...
متن کاملPrograms for Applying Symmetries of PDEs
In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO are described which aim at the utilization of infinitesimal symmetries of differential equations. The purpose of QUASILINPDE is the general solution of quasilinear PDEs. This procedure is used by APPLYSYM for the application of point symmetries for either • calculating similarity variables to perform a point transformation which lower...
متن کاملFrobenius integrable decompositions for ninth-order partial differential equations of specific polynomial type
Keywords: Frobenius integrable decompositions Partial differential equations Differential polynomials Bäcklund transformations Ordinary differential equations Nonlinearity a b s t r a c t Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius i...
متن کاملNon-autonomous Hénon-Heiles Systems
Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivativ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013