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Journal Articles

A Posteriori Error Analysis of Defect Correction Method for Singular Perturbation Problems With Discontinuous Coefficient and Point Source

Aditya Kaushik, Shivani Jain
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. September 2024, 19(9): 091005.
Paper No: CND-24-1044
https://doi.org/10.1115/1.4065900
Published Online: July 25, 2024
View Article titled, A Posteriori Error Analysis of Defect Correction Method for Singular Perturbation Problems With Discontinuous Coefficient and Point Source
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Topics: Error analysis, Errors, Stability, Numerical analysis, Boundary layers
Journal Articles

α-Robust Error Analysis of L2- 1 σ Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation

Pari J. Kundaliya
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. May 2024, 19(5): 051004.
Paper No: CND-23-1173
https://doi.org/10.1115/1.4065011
Published Online: March 21, 2024
View Article titled, α-Robust Error Analysis of L2- 1 σ Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation
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Topics: Diffusion (Physics), Errors, Error analysis, Theorems (Mathematics)
Journal Articles

Improved Numerical Approach for Bagley–Torvik Equation Using Fractional Integral Formula and Adams–Moulton Method

Yonghyeon Jeon, Sunyoung Bu
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. May 2024, 19(5): 051005.
Paper No: CND-23-1250
https://doi.org/10.1115/1.4065012
Published Online: March 21, 2024
View Article titled, Improved Numerical Approach for Bagley–Torvik Equation Using Fractional Integral Formula and Adams–Moulton Method
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Topics: Errors, Integral equations, Laplace transforms, Approximation, Error analysis
Journal Articles

Numerical Treatment for the Solution of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method

P. K. Singh, S. Saha Ray
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. January 2024, 19(1): 011004.
Paper No: CND-22-1311
https://doi.org/10.1115/1.4063885
Published Online: November 15, 2023
View Article titled, Numerical Treatment for the Solution of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method
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Topics: Differential equations, Polynomials, Algebra, Error analysis
Journal Articles

Exact Solutions of Systems of Nonlinear Time-Space Fractional Partial Differential Equations Using an Iterative Method

Manoj Kumar
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. October 2023, 18(10): 101003.
Paper No: CND-22-1295
https://doi.org/10.1115/1.4062910
Published Online: July 26, 2023
View Article titled, Exact Solutions of Systems of Nonlinear Time-Space Fractional Partial Differential Equations Using an Iterative Method
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Topics: Diffusion (Physics), Partial differential equations, Error analysis, Iterative methods
Journal Articles

Singular and Nonsingular Kernels Aspect of Time-Fractional Coupled Spring-Mass System

Rajarama Mohan Jena, Snehashish Chakraverty
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. February 2022, 17(2): 021001.
Paper No: CND-21-1192
https://doi.org/10.1115/1.4052788
Published Online: November 17, 2021
View Article titled, Singular and Nonsingular Kernels Aspect of Time-Fractional Coupled Spring-Mass System
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Topics: Differential equations, Interpolation, Polynomials, Springs, Stability, Error analysis
Journal Articles

Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation

Kushal Dhar Dwivedi, Rajeev, Subir Das, Dumitru Baleanu
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. June 2020, 15(6): 061005.
Paper No: CND-19-1288
https://doi.org/10.1115/1.4046879
Published Online: April 27, 2020
View Article titled, Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation
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Topics: Diffusion (Physics), Polynomials, Spacetime, Error analysis, Boundary-value problems, Approximation, Numerical analysis
Journal Articles

Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals

Dongling Wang, Aiguo Xiao
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2013, 8(2): 021018.
Paper No: CND-12-1132
https://doi.org/10.1115/1.4007858
Published Online: November 15, 2012
View Article titled, Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals
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Topics: Errors, Numerical analysis, Theorems (Mathematics), Error analysis, Boundary-value problems