An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation

Sazaklioglu, Ali Ugur

doi:10.1016/j.apnum.2024.02.001

Applied Numerical Mathematics

2024

DOI: 10.1016/j.apnum.2024.02.001

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An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation

Ali Ugur Sazaklioglu

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2024

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Cited by 2 publications

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Computational Analysis of Parallel Techniques for Nonlinear Biomedical Engineering Problems

Shams,

Carpentieri

2024

Algorithms

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In this study, we develop new efficient parallel techniques for solving both distinct and multiple roots of nonlinear problems at the same time. The parallel techniques represent an innovative contribution to the discipline, with local convergence of the ninth order. Theoretical research shows the rapid convergence and effectiveness of the proposed parallel schemes. To assess the suggested scheme’s stability and consistency, we look at certain biomedical engineering applications, such as osteoporosis in Chinese women, blood rheology, and differential equations. Overall, detailed analyses of convergence behavior, memory utilization, computational time, and percentage computational efficiency show that the novel parallel techniques outperform the traditional methods. The proposed methods would be more suitable for large-scale computational problems in biomedical applications due to their advantages in memory efficiency, CPU time, and error reduction.

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Computational Analysis of Parallel Techniques for Nonlinear Biomedical Engineering Problems

Shams,

Carpentieri

2024

Algorithms

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The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

Shen,

Yang,

Zhang

2024

Mathematics

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In this paper, the numerical solution for two-dimensional nonlinear parabolic equations is studied using an alternating-direction implicit (ADI) Crank–Nicolson (CN) difference scheme. Firstly, we use the CN format in the time direction, and then use the CN format in the space direction before discretizing the second-order center difference quotient. In addition, we strictly prove that the proposed ADI difference scheme has unique solvability and is unconditionally stable and convergent. The extrapolation method is further applied to improve the numerical solution accuracy. Finally, two numerical examples are given to verify our theoretical results.

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An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation

Cited by 2 publications

References 45 publications

Computational Analysis of Parallel Techniques for Nonlinear Biomedical Engineering Problems

Computational Analysis of Parallel Techniques for Nonlinear Biomedical Engineering Problems

The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

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