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A High-Order Iterative Scheme for a Nonlinear Pseudoparabolic Equation and Numerical Results

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  • Nguyen Huu Nhan
  • Tran Trinh Manh Dung
  • Le Thi Mai Thanh
  • Le Thi Phuong Ngoc
  • Nguyen Thanh Long

Abstract

In this paper, by applying the Faedo-Galerkin approximation method and using basic concepts of nonlinear analysis, we study the initial-boundary value problem for a nonlinear pseudoparabolic equation with Robin–Dirichlet conditions. It consists of two main parts. Part 1 is devoted to proof of the unique existence of a weak solution by establishing an approximate sequence based on a - order iterative scheme in case of , or a single-iterative scheme in case of . In Part 2, we begin with the construction of a difference scheme to approximate of the - order iterative scheme, with . Next, we present numerical results in detail to show that the convergence rate of the 2-order iterative scheme is faster than that of the single-iterative scheme.

Suggested Citation

  • Nguyen Huu Nhan & Tran Trinh Manh Dung & Le Thi Mai Thanh & Le Thi Phuong Ngoc & Nguyen Thanh Long, 2021. "A High-Order Iterative Scheme for a Nonlinear Pseudoparabolic Equation and Numerical Results," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, March.
    • Handle: RePEc:hin:jnlmpe:8886184
    DOI: 10.1155/2021/8886184
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