چکیده مقاله
The study of fractional Sturm Liouville problems has gained significant attention due to their wide range of applications in various fields, including physics, engineering, and finance Solving these problems involves computing the eigenvalues and eigenfunctions associated with the fractional differential equations However, obtaining accurate numerical approximations of these eigenvalues and eigenfunctions poses a significant challenge This paper presents an efficient approach for approximating eigenvalues and eigenfunctions in fractional Sturm Liouville problems The proposed method combines the advantages of spectral methods and iterative techniques to achieve accurate and reliable results Firstly, the problem domain is discretized using a suitable spectral basis, such as Chebyshev or Legendre polynomials, which offer excellent approximation properties The fractional differential operator is then approximated using a suitable fractional difference formula, such as the Grünwald Letnikov or Caputo discretization To compute the eigenvalues, an iterative algorithm is employed, such as the power method or the inverse iteration method These methods efficiently extract the dominant eigenvalues and corresponding eigenfunctions by iteratively updating an initial guess The accuracy and efficiency of the proposed approach are demonstrated through numerical experiments on a variety of fractional Sturm Liouville problems Comparisons with existing methods highlight the superiority of the proposed method in terms of convergence rate and computational cost In conclusion, this paper presents a novel and efficient approach for approximating eigenvalues and eigenfunctions in fractional Sturm Liouville problems The combination of spectral methods, fractional difference formulas, and iterative algorithms yields accurate results while minimizing computational effort This research contributes to the advancement of numerical techniques in fractional calculus and extends their applicability in diverse scientific and engineering domains
کلیدواژهها
نویسندگان
Loghman Sedaghat
master
شیوه ارجاع
Sedaghat, Loghman,1402,Efficient Numerical Approximation of Eigenvalues and Eigenfunctions in Fractional Sturm-Liouville Problems,International conference of humanities, educational sciences, law and social sciences
ارائهشده در
مجموعه مقالات کنفرانس بین المللی علوم انسانی ، علوم آموزشی ، حقوق و علوم اجتماعی28 فروردین 1402