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التماثيل في المعادلات التفاضلية == SYMMETRY OF DIFFERENTIAL EQUATIONS
Author name:
طلعت جاسم محمود
Supervisor name:
انعام عبد الرحمن ملوكي
General topic:
Mathematics
Specific topic:
Differential Equations
Degree:
Master
University:
Mustansiriyah University - College Of Science - Department Of Mathematics
Language:
English
University location:
Baghdad
First pages:
27T1158 - p.pdf
Abstract:
Symmetries of a system of di erential equations are transformations, which transform the family of solutions of a system of di erential equations to itselves. In fact, the theory of symmetry of di erential equations in arguably one of the most successful methods in nding the solutions of di erential equations, this theory uni es a number of previously unrelated methods into a single method. However, as with all theories, there are instances in which it provide no useful information. Thus extensions and generalizations of the method are necessary to broader the class of equations analyzed by this method. In this thesis, a general view about the subject of classical symmetry and its generalization on di erential equations is considered, classical symmetry for many di erential equations using Lie's algorithm or Maple program have been calculated. A comparison between the classical and nonclassical symmetries, and we have found, some nonclassical symmetries of the Benjamin Bona Mahony equation and some weak symmetries for this equation, which have been used to nd exact solution for this equation.Moreover, this thesis studied some applications for symmetry which can be used to solve di erential equations, such as : Finding the hidden symmetries and their origins (sources) for some ODEs and for Benjamin Bona Mahony equation, nding discrete symmetry, by using continuous symmetry, and we got new symmetries which can be considered as a composition of continuous and discrete symmetries, solving boundary value problems of di erential equation and nding the boundary conditions which are consistent with symmetry of the di erential equation. Moreover, the Clarkson problem was discussed in order to know whether the di erential equation possess a nonclassical symmetries, without solving the problem and that by using hidden symmetries.
