Loading [MathJax]/jax/output/CommonHTML/jax.js
Search button
Close Search Advanced
Journals
Resources
About Us
Open Access
Journals
Resources
About Us
Open Access
Go to previous page

An L∞-Error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

An $L^∞$-Error Estimate for the $h$-$p$ Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems
Preview
Add to basket

Year:    2015

East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 4 : pp. 301–311

Abstract

The h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

Share Journal
Cite article

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.310315.070815a

East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 4 : pp. 301–311

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Initial value problems h−p version time stepping method continuous Petrov-Galerkin method error bound.

  1. BDF ADI orthogonal spline collocation scheme for the fractional integro-differential equation with two weakly singular kernels

    Qiao, Leijie | Xu, Da

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 12 P.3807

    https://doi.org/10.1016/j.camwa.2019.06.002 [Citations: 25]

  2. hp-version C1-continuous Petrov–Galerkin method for nonlinear second-order initial value problems with application to wave equations

    Wang, Lina | Zhang, Mingzhu | Tian, Hongjiong | Yi, Lijun

    IMA Journal of Numerical Analysis, Vol. (2024), Iss.

    https://doi.org/10.1093/imanum/drae036 [Citations: 0]

  3. A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation

    Qiao, Leijie | Qiu, Wenlin | Tang, Bo

    Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 2 P.1333

    https://doi.org/10.1002/num.22936 [Citations: 10]

  4. An hp-version of the C0-continuous Petrov-Galerkin time stepping method for nonlinear second-order initial value problems

    Wei, Yichen | Yi, Lijun

    Advances in Computational Mathematics, Vol. 46 (2020), Iss. 4

    https://doi.org/10.1007/s10444-020-09800-3 [Citations: 5]

  5. BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions

    Wang, Ruru | Yan, Yubin | Hendy, A.S. | Qiao, Leijie

    Computers & Mathematics with Applications, Vol. 155 (2024), Iss. P.126

    https://doi.org/10.1016/j.camwa.2023.12.008 [Citations: 0]

  6. An h-p Version of the Continuous Petrov–Galerkin Method for Nonlinear Delay Differential Equations

    Meng, Tingting | Yi, Lijun

    Journal of Scientific Computing, Vol. 74 (2018), Iss. 2 P.1091

    https://doi.org/10.1007/s10915-017-0482-z [Citations: 12]

  7. Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type

    Qiao, Leijie | Guo, Jing | Qiu, Wenlin

    Computers & Mathematics with Applications, Vol. 123 (2022), Iss. P.89

    https://doi.org/10.1016/j.camwa.2022.08.014 [Citations: 20]

  8. An hp-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays

    Wei, Yichen | Sun, Tao | Yi, Lijun

    Journal of Computational and Applied Mathematics, Vol. 364 (2020), Iss. P.112348

    https://doi.org/10.1016/j.cam.2019.112348 [Citations: 3]

  9. An h-p version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations

    Xie, Jinghua | Yi, Lijun

    Applied Numerical Mathematics, Vol. 143 (2019), Iss. P.1

    https://doi.org/10.1016/j.apnum.2019.03.015 [Citations: 5]

  10. An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation

    Qiao, Leijie | Wang, Zhibo | Xu, Da

    Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.199

    https://doi.org/10.1016/j.apnum.2020.01.003 [Citations: 45]

  11. Legendre-Petrov-Galerkin Chebyshev spectral collocation method for second-order nonlinear differential equations

    Gao, Qiyi | Wu, Hua

    Discrete and Continuous Dynamical Systems - B, Vol. 28 (2023), Iss. 3 P.2246

    https://doi.org/10.3934/dcdsb.2022166 [Citations: 3]