Simetriler yardımıyla diferensiyel denklemlerin çözümü
Küçük Resim Yok
Tarih
2003
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
ÖZET Sıradan diferansiyel denklemlerin çözüm yöntemlerinden biride denklemlerin simetriler yardımı ile çözümlerinin bulunmasıdır. Bu çalışmaların I, II, ve III. Bölümlerinde diferansiyel denklemlerle ilgili genel bilgiler verilmiş, Nokta dönüşümleri, dönüşüm kuralları, üreteçlerin normal formları, dönüşümlerin ve üreteçlerin genişlemeleri, dönüşümlerin çok parametreli grupları ve üreteçleri, simetri tanımları, diferansiyel denklemlerin Lie nokta simetrileri verilmiştir. IV. Bölümde adi türevli diferansiyel denklemlerin Lie nokta simetrilerinin bulunması incelenmiş, birinci, ikinci ve yüksek mertebeden diferansiyel denklemlerin simetrileri bulunmuştur. V. ve VI. Bölümlerde Lie nokta simetrilerinin kullanılması ve bir simetrisi bilinen diferansiyel denklemlerin çözümlerinin nasıl yapılacağı araştırılarak konu tartışılmıştır. Ek A, Ek B, Ek C, de ise Lie nokta simetrilerinin bulunması, simetrilerin kullanılması ve simetrileri bilinen diferansiyel denklemlerin çözümleri ile ilgili örnekler verilmiştir.
SUMMARY One of the methods of solving the ordinary differential equations is to find the solutions of the equations by the help of the symmetries. At the 1th, 2th and 3lh chapters of these studies, general information about the differential equations was given and the point transformations, the rules of the transformation, the normal forms of the generator, extending of the transformators and generators, groups with polyparameter and generators of the transformations, the definitions of the symmetry, Lie point symmetries of the differential equations were given. At the 4th chapter, finding of Lie point symmetries of the differential equations with the inferior derivation was scrutinized, and the symmetries of the differential equations from the first, second and high degree were found At the 5th and 6,h chapters, use of the Lie point symmetries and how the solutions of the differantial equations, whose one symmetry is known will be done, was researched and th subject was discussed. At the appendixes A-B-C, finding of the Lie point symmetries, use of the symmetries and the examples related with solututions of the differantial equations whose symmetries are known were given.
SUMMARY One of the methods of solving the ordinary differential equations is to find the solutions of the equations by the help of the symmetries. At the 1th, 2th and 3lh chapters of these studies, general information about the differential equations was given and the point transformations, the rules of the transformation, the normal forms of the generator, extending of the transformators and generators, groups with polyparameter and generators of the transformations, the definitions of the symmetry, Lie point symmetries of the differential equations were given. At the 4th chapter, finding of Lie point symmetries of the differential equations with the inferior derivation was scrutinized, and the symmetries of the differential equations from the first, second and high degree were found At the 5th and 6,h chapters, use of the Lie point symmetries and how the solutions of the differantial equations, whose one symmetry is known will be done, was researched and th subject was discussed. At the appendixes A-B-C, finding of the Lie point symmetries, use of the symmetries and the examples related with solututions of the differantial equations whose symmetries are known were given.
Açıklama
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Yüksek Lisans
Yüksek Lisans
Anahtar Kelimeler
Matematik, Mathematics
