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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations \linebreak (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^\infty$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.
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참고문헌 (20)
참고문헌 신청
P. Baratella / 2004 / A new approach to the numerical solution of weakly singular Volterra integral equations / J. Comput. Appl. Math 163(2):401~418
C. Canuto / 2006 / Spectral Methods, Fundamentals in single domains / Springer-Verlag
Y. Chen / 2009 / Spectral methods for weakly singular Volterra integral equations with smooth solutions / J. Comput. Appl. Math 233(4):938~950
Y. Chen / 2010 / Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equation with a weakly singular kernel / Math. Comp 79(269):147~167
D. Colton / 1998 / Inverse Acoustic and Electromagnetic Scattering Theory / Springer-Verlag
C. Canuto / 2006 / Spectral Methods, Fundamentals in single domains / Springer-Verlag
Y. Chen / 2009 / Spectral methods for weakly singular Volterra integral equations with smooth solutions / J. Comput. Appl. Math 233(4):938~950
Y. Chen / 2010 / Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equation with a weakly singular kernel / Math. Comp 79(269):147~167
D. Colton / 1998 / Inverse Acoustic and Electromagnetic Scattering Theory / Springer-Verlag
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