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Deng, Nan; Cao, Wanrong; Pang, Guofei

On numerical methods to second-order singular initial value problems with additive white noise. (English) Zbl 1492.65021

J. Comput. Appl. Math. 416, Article ID 114539, 22 p. (2022).

MSC: 65C30 34F05 60H10 60H35 65L05 65L20

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Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.; Wurm, Stefan

On nonlinear singular BVPs with nonsmooth data. I: Analytical results. (English) Zbl 1397.34048

Appl. Numer. Math. 130, 23-50 (2018).

MSC: 34B16 65L60

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Hasan, M. Kamrul; Ahamed, M. Suzan; Haque, B. M. Ikramul; Alam, M. S.; Hossain, M. Bellal

A higher order implicit method for numerical solution of singular initial value problems. (English) Zbl 1442.65128

Giri, Debasis (ed.) et al., Mathematics and computing. Third international conference, ICMC 2017, Haldia, India, January 17–21, 2017. Proceedings. Singapore: Springer. Commun. Comput. Inf. Sci. 655, 255-264 (2017).

MSC: 65L06 34A12

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Burkotová, Jana; Rachunková, Irena; Weinmüller, Ewa B.

On singular BVPs with nonsmooth data: analysis of the linear case with variable coefficient matrix. (English) Zbl 1357.65098

Appl. Numer. Math. 114, 77-96 (2017).

MSC: 65L10 34B05

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Abu Arqub, Omar

Reproducing kernel algorithm for the analytical-numerical solutions of nonlinear systems of singular periodic boundary value problems. (English) Zbl 1394.65058

Math. Probl. Eng. 2015, Article ID 518406, 13 p. (2015).

MSC: 65L10 34A45

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Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.

On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity. (English) Zbl 1316.34025

Bound. Value Probl. 2014, Paper No. 183, 34 p. (2014).

Reviewer: Petio S. Kelevedjiev (Sliven)

MSC: 34B16 34A12 34A30 34B05 65L10

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OA License

Dick, Alexander; Koch, Othmar; März, Roswitha; Weinmüller, Ewa

Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point. (English) Zbl 1262.65092

Math. Comput. 82, No. 282, 893-918 (2013).

MSC: 65L80 65L60 65L20 65L70 34A09

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Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa

Collocation methods for index 1 DAEs with a singularity of the first kind. (English) Zbl 1196.65134

Math. Comput. 79, No. 269, 281-304 (2010).

MSC: 65L80 65L60 65L70 34A05

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Cash, J.; Kitzhofer, G.; Koch, O.; Moore, G.; Weinmüller, E.

Numerical solution of singular two point BVPs. (English) Zbl 1191.65099

JNAIAM, J. Numer. Anal. Ind. Appl. Math. 4, No. 1-2, 129-149 (2009).

MSC: 65L10 65L60 34B16 65Y20

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Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa

New a posteriori error estimates for singular boundary value problems. (English) Zbl 1082.65079

Numer. Algorithms 40, No. 1, 79-100 (2005).

Reviewer: Pavol Chocholatý (Bratislava)

MSC: 65L70 65L10 34B16 65L60

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Auzinger, Winfried; Koch, Othmar; Weinmüller, Ewa

Analysis of a new error estimate for collocation methods applied to singular boundary value problems. (English) Zbl 1087.65082

SIAM J. Numer. Anal. 42, No. 6, 2366-2386 (2005).

Reviewer: Pat Lumb (Chester)

MSC: 65L70 65L10 34B16 65L05 62L20 65L50

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Koch, Othmar

Asymptotically correct error estimation for collocation methods applied to singular boundary value problems. (English) Zbl 1076.65073

Numer. Math. 101, No. 1, 143-164 (2005).

Reviewer: Manuel Calvo (Zaragoza)

MSC: 65L70 65L10 65L60 34B16

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Auzinger, W.; Koch, O.; Weinmüller, E.

Efficient mesh selection for collocation methods applied to singular BVPs. (English) Zbl 1069.65093

J. Comput. Appl. Math. 180, No. 1, 213-227 (2005).

MSC: 65L60 65L10 65L50 34B16 65L70

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Koch, Othmar; Weinmüller, Ewa

Analytical and numerical treatment of a singular initial value problem in avalanche modeling. (English) Zbl 1089.34004

Appl. Math. Comput. 148, No. 2, 561-570 (2004).

MSC: 34A12 65L05 74L05 86A60

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Koch, Othmar; Weinmüller, Ewa B.

The convergence of shooting methods for singular boundary value problems. (English) Zbl 1013.65081

Math. Comput. 72, No. 241, 289-305 (2003).

Reviewer: Pavol Chocholatý (Bratislava)

MSC: 65L10 34B16 65L20

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Koch, Othmar; Weinmüller, Ewa B.

Iterated defect correction for the solution of singular initial value problems. (English) Zbl 0989.65068

SIAM J. Numer. Anal. 38, No. 6, 1784-1799 (2001).

Reviewer: K.Burrage (St.Lucia)

MSC: 65L05 65L20 34A34

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Found 16 Documents (Results 1–16)

On numerical methods to second-order singular initial value problems with additive white noise. (English) Zbl 1492.65021

On nonlinear singular BVPs with nonsmooth data. I: Analytical results. (English) Zbl 1397.34048

A higher order implicit method for numerical solution of singular initial value problems. (English) Zbl 1442.65128

On singular BVPs with nonsmooth data: analysis of the linear case with variable coefficient matrix. (English) Zbl 1357.65098

Reproducing kernel algorithm for the analytical-numerical solutions of nonlinear systems of singular periodic boundary value problems. (English) Zbl 1394.65058

On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity. (English) Zbl 1316.34025

Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point. (English) Zbl 1262.65092

Collocation methods for index 1 DAEs with a singularity of the first kind. (English) Zbl 1196.65134

Numerical solution of singular two point BVPs. (English) Zbl 1191.65099

New a posteriori error estimates for singular boundary value problems. (English) Zbl 1082.65079

Analysis of a new error estimate for collocation methods applied to singular boundary value problems. (English) Zbl 1087.65082

Asymptotically correct error estimation for collocation methods applied to singular boundary value problems. (English) Zbl 1076.65073

Efficient mesh selection for collocation methods applied to singular BVPs. (English) Zbl 1069.65093

Analytical and numerical treatment of a singular initial value problem in avalanche modeling. (English) Zbl 1089.34004

The convergence of shooting methods for singular boundary value problems. (English) Zbl 1013.65081

Iterated defect correction for the solution of singular initial value problems. (English) Zbl 0989.65068

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