지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
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Investigation of the numerical solution of singularly perturb- ed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges.
To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.
목차
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참고문헌 (28)
참고문헌 신청
L. R. Abrahamsson / 1977 / A priori estimates for solutions of singular perturbations with a turning point / Stud. Appl. Math 56(1):51~69
N. Adzic / 1992 / Spectral approximation for single turning point problem / Z. Angew. Math. Mech 72(6):621~624
N. Adzic / 1993 / Jacobi approximate solution of the boundary layer problem / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 23(1):347~359
N. Adzic / 1994 / Domain decomposition for spectral approximation of the layer solution / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 24(1):347~357
N. Adzic / 1995 / Jacobi polynomials in spectral approximation for shock layer problems / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 25(1):53~65
N. Adzic / 1992 / Spectral approximation for single turning point problem / Z. Angew. Math. Mech 72(6):621~624
N. Adzic / 1993 / Jacobi approximate solution of the boundary layer problem / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 23(1):347~359
N. Adzic / 1994 / Domain decomposition for spectral approximation of the layer solution / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 24(1):347~357
N. Adzic / 1995 / Jacobi polynomials in spectral approximation for shock layer problems / Zb. Rad. Prirod.-Mat. Fak. Ser. Math 25(1):53~65
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