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Ulsan National Institute of Science and Technology

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작성일 : 15-02-24 15:15
Congratulations to our 2015 graduate student
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Congratulations to the graduate student Kyungduk Park who earned master's degrees from the UNIST Mathematical Sciences on Feb 24, 2015.

His thesis is "Multistage Shifted JACOBI Spectral Method for solving linear & nonlinear Fractional Differential Equations". [Link]


항목내용항목언어
제목Multistage Shifted JACOBI Spectral Method for solving linear & nonlinear Fractional Differential Equations 
저자Kyung Duk Park 
저자(제2언어)박경덕 
소속Ulsan National Institute of Science and Technology (UNIST) 
초록/요약In this work, we developed a new numerical method based on the shifted jacobi polynomials for solving linear and nonlinear initial value problem and boundary value problem of fractional differential equation. We extend the conventional spectral approaches such as the Shifted Jacobi Tau(SJT) method for linear problem and the Shifted Jacobi Collocation(SJC) method for nonlinear problem, by using the multistage methodology. These methods are called the Multistage Shifted Jacobi Tau(M-SJT) and the Multistage Shifted Jacobi Collocation(M-SJC) method,respectively. From the several illustrative examples, the advantages of using the proposed methods are discussed for the initial value problem and we compare the proposed methods with exact solution and conventional spectral approaches. 

In addition, we extend the proposed methods for solving nonlinear boundary value problem of the fractional differential equations. Since all proposed methods are developed for solving the linitial problem, it is necessary to convert the boundary problem to the initial problem. Here we adopt the nonlinear shooting method combined with M-SJC. From the numerical example, the advantages of using the proposed methods are discussed for the nonlinear boundary value problem and we compare the proposed methods with exact solution and conventional spectral approaches.
영어
목차I Introduction 
II Preliminary 
  2.1 Fractional Calculus 
  2.2 Shifted Jacobi Polynomials 
III Initial Value Problem of Fractional Di erential Equation 
  3.1 Model Problem 
      3.1.1 Shifted Jacobi Tau (SJT) method for initial value problem 
      3.1.2 Multistage Shifted Jacobi Tau (M-SJT) method for initial value problem 
      3.1.3 Numerical results of the linear FDE 
  3.2 Model Problem 
      3.2.1 Shifted Jacobi collocation (SJC) method for initial value problem 
      3.2.2 Mutistage shifted Jacobi collocation (M-SJC) method for initial value problem 
      3.2.3 Numerical results of the nonlinear FDE 
IV Boundary Value Problem of Fractional Di erential Equation 
  4.1 Model Problem 
  4.2 Shifted Jacobi collocation (SJC) method for boundary value problem 
  4.3 Multistage Shifted Jacobi collocation (M-SJC) method for boundary value problem 
      4.3.1 Shooting method for the boundry value problem 
  4.4 Numerical results of Fractional Boundary Value Di erential Equation 
V Conclusion 
References
 
발행기관Graduate school of UNIST' 
지도교수Jang, Bongsoo 
발행년도2015 
학위수여년월2015. 2 
세부유형Dissertation 
학위명Master 
학과 및 전공GraduateSchoolofUNIST DepartmentOfMathematicalSciences 
원문크기853801 bytes 
식별자유형고유URL 
실제URIhttp://www.dcollection.net/handler//000001924595 
본문언어eng 
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