Hasil Pencarian  ::  Simpan CSV :: Kembali

"ABSTRAKTulisan ini membahas sebuah metode untuk menyelesaikan persamaan diferensial parsial dimana persamaannya mengandung parameter Є. Metode ini menggunakan deret pangkat dari Є sebagai deret perturbasi. Kemudian persamaannya dikelompokkan menurut Єn , dengan menyamakan koefisien dari Єn = 0 maka pemecahannya didapatkan dengan cara rekursi yaitu : Pertama didapat solusi Uo dimana Uo adalah solusi persamaan yang direduksi setelah Uo didapat maka U1 akan didapat sehingga U = U1Є + 0 . (Є2). Hasil dari metode ini dapat dibandingkan dengan hasil eksata."

"Pada tesis ini dibahas mengenai sistem predator-prey dengan tingkat kelahiran prey jauh lebih kecil dibandingkan tingkat kematian predator dan mengasumsikan bahwa populasi prey terbatas, sehingga ditambahkan faktor kapasitas lingkungan ke populasi prey. Karena perbedaan rentang waktu regenerasi antara predator dan prey relatif tinggi, sistem memiliki struktur fast-slow. Struktur fast-slow pada model dianalisis dengan menggunakan geometric singular perturbation theory (GSPT) yang membagi sistem menjadi fast subsystem dan slow subsystem. Dalam tesis ini, dipelajari keberadaan solusi ekuilibrium dan stabilitasnya, dan juga perilaku solusi di sekitar critical manifold. Selanjutnya, dengan menggunakan fungsi entry-exit diperoleh hubungan antara solusi fast subsystem dan slow subsystem secara analitis.

---

In this thesis we discuss the predator-prey system with the birth rate of the prey is much smaller compared to the predator mortality rate where it is assumed that the population of prey is limited. Therefore, an environmental carrying capacity factor is added to the prey population. Due to the difference in regeneration’s timescales between predator and prey, some solutions of the system may have a fast-slow structure. The fast-slow structure of the model is analyzed using the geometric singular perturbations theory (GSPT) which divides the system into fast and slow subsystem. In this thesis, we study the existence of the equilibrium solutions and their stability, and also the behaviour of the solutions near critical manifold. Furthermore, using an entry-exit function we obtain the connection between the solutions of the slow subsystem and the fast subsystem analytically."

"ABSTRAKOpsi saham merupakan salah satu jenis sekuritas derivatif yang nilai kontraknya bergantung pada nilai saham yang tercantum pada kontrak opsi. Opsi saham Asia termasuk ke dalam jenis opsi eksotik yang nilainya dipengaruhi oleh rata-rata nilai saham sepanjang masa hidup opsi. Dalam skripsi ini rata-rata nilai aset yang digunakan adalah rata-rata geometrik. Nilai saham yang digunakan dalam skripsi ini akan mengikuti model CEV Constant Elasticity of Variance yang merupakan bentuk umum dari model Black-Scholes yang terkenal. Dalam menentukan nilai opsi secara analitik dengan model CEV sangatlah sulit maka dari itu nilai dari opsi Asia dimodelkan ke dalam persamaan diferensial parsial. Persamaan diferensial parsial untuk opsi Asia nantinya akan diselesaikan dengan metode perturbasi. Metode perturbasi yang digunakan adalah metode perturbasi regular. Pada akhirnya akan dihasilkan formula untuk menentukan harga opsi call Asia dengan model CEV dan rata-rata geometrik

---

ABSTRACTStock options are one type of derivative securities whose contract value depends on the value of the shares listed on the option contract. Asian stock options fall into the type of exotic options whose value is affected by the average share value throughout the lifetime of the option. In this thesis the average asset value used is the geometric average. The stock value used in this thesis will follow the CEV Constant Elasticity of Variance model which is a general form of the famous Black Scholes model. In determining the analytic option value with the CEV model it is very difficult, because of that the value of the Asian option is modeled into a partial differential equation. Partial differential equations for Asian options will be solved by perturbation method. The perturbation method used is a regular perturbation method. In the end a formula will be generated to determine the price of Asian call option with CEV model and geometric mean."

"Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems."

"Chiral perturbation theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques."

"Most of the results are closely connected with PDEs, and the authors' approach presents a powerful method for studying the asymptotic behavior of the solutions of initial-boundary value problems for corresponding PDEs."

"Perturbation Bounds for Matrix Eigenvalues contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to special classes. The book emphasis on sharp estimates, general principles, elegant methods, and powerful techniques, makes it a good reference for researchers and students."

"This book is the third installment in a series of four self-contained English translations of the classic and definitive treatment. Key features, complete and unabridged presentation with recent advances and additional notes, annotations by the translators provide insights into the nature of science and mathematics in the late 19th century, each volume interweaves theory and applications.The theory of the top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this series of books a thorough and insightful account. Other volumes in the series include the introduction to the kinematics and kinetics of the top, development of a theory of the heavy symmetric top, and technical applications of the theory of the top."

"Pada suatu sistem tenaga listrik jika terjadi suatu gangguan yang besar misalnya hilangnya beban karena terputusnya saluran transmisi utama atau adanya gangguan tiga fasa ke tanah, maka mesin-mesin (generator) akan mengalami suatu keadaan transient yang mengakibatkan mesin berosilasi sebeium mencapai keadaan kestabilan yang bam atau bahkan kernudian mesin itu terlepas dari sistem karena kehilangan keserempakannya, Kehilangan keserempakan suatu mesin dapat dicegah jika gangguan yang terjadi dapat dihilangkan sebelum terlampauinya waktu pemutusan kritis yaitu waktu pemutusan gangguan yang masih memungkinkan mesin-mesin kembali kekeadaan kestabilan- Lamanya keadaan transient hanya merupakan waktu yang sin gkat kurang dad 1 detik sehingga diperlukan suatu metoda yang mernadai untuk menangani masalah kestabilan ini. Untuk sistem yang terdiri dari 2 mesin prediksi kestabilan dapat djlalcukan dengan kriteria sama luas (Equai Area Criterion) sedangkan untuk suatu sistem dengan banyak mesin dengan tersedianya alat komputasi digital yang makin canggih, rnetode penyelesaian seoara langsung persamaan ayunan dapat dilakukan. Untuk membantu penyelesaian masalah ini telah dibuat suatu program numerik dengan rnenggunakan bahasa pascal (Borland Delphi ver. 3.0) dan alur program menggunakan metode Euler yang Diperbaiki dengan Iangkah iterasi sebesar 0.001 detik."

"Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point."