Numerical study of the fractional fourth-order evolution problems with weak singularity arises in chemical systems

Authors: Taneja, Komal, Chawla, Reetika, Kumar, Devendra, Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:1287-1311

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Fractional derivatives and integrals, graded mesh, time-fractional fourth order equation, stability and convergence, Numerical methods for initial value problems involving ordinary differential equations, evolution problems, quintic trigonometric B-spline, Caputo derivative, Numerical computation using splines

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Access URL: https://zbmath.org/8035161
https://doi.org/10.1007/s10910-025-01718-9

Investigation of real-world second-order singular differential equations by optimal homotopy analysis technique

Authors: Singh, Randhir, Datta, Prabal, Guleria, Vandana, Sahoo, Nirupam

Source: Journal of Mathematical Chemistry. 63:962-981

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, temperature distribution, Applications of boundary value problems involving ordinary differential equations, singular differential equation, series solution, Singular nonlinear boundary value problems for ordinary differential equations, thermal explosion, homotopy analysis method, Adomian decomposition method, Theoretical approximation of solutions to ordinary differential equations

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Approximation of a function with bounded derivatives of first and second order by the extended Sine-Cosine wavelet expansion with applications: Approximation of a function with bounded derivatives of first and second order by the extended sine-cosine wavelet expansion with applications

Authors: Sharma, Vivek Kumar, Sharma, Virendra, Singh, Sonoo

Source: Electronic Journal of Mathematical Analysis and Applications. 13:1-26

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, extended sine-cosine wavelet, Numerical methods for wavelets, Nontrigonometric harmonic analysis involving wavelets and other special systems, wavelet approximation, Numerical methods for integral equations, functions of bounded derivatives

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Access URL: https://zbmath.org/8036659
https://doi.org/10.21608/ejmaa.2025.321121.1267

An efficient computational technique and its convergence analysis for a class of doubly singular boundary value problems

Authors: Roul, Pradip, Agarwal, Ravi P.

Source: Journal of Mathematical Chemistry. 63:502-525

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Singular nonlinear boundary value problems for ordinary differential equations, undetermined coefficients, doubly SBVP, convergence control parameter, fast convergent

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Access URL: https://zbmath.org/7990899
https://doi.org/10.1007/s10910-024-01685-7

Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology

Authors: Giacomo Rosilho de Souza, Marcus J. Grote, Simone Pezzuto, Rolf Krause

Source: ESAIM: Mathematical Modelling and Numerical Analysis

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, 65L04, 65L06, 65L10, 65L20, Numerical Analysis (math.NA), electrophysiology, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, local time-stepping, monodomain model, multirate explicit stabilized methods, ionic model, Numerical methods for stiff equations, Multirate explicit stabilized methods, Rush–Larsen, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for ordinary differential equations, Rush-Larsen

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Access URL: http://arxiv.org/abs/2401.01745
https://zbmath.org/7971354
https://doi.org/10.1051/m2an/2024030
https://hdl.handle.net/11572/442124
https://www.esaim-m2an.org/articles/m2an/abs/2024/06/m2an230300/m2an230300.html
https://doi.org/10.1051/m2an/2024030

Construction of high order numerical methods for solving fourth order nonlinear boundary value problems

Authors: Dang, Quang A., Thanh Huong Nguyen, Vinh Quang Vu

Source: Numerical Algorithms. 99:323-354

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Nonlinear boundary value problems for ordinary differential equations, iterative method, high order numerical methods, fourth order nonlinear boundary value problems

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A novel fixed point approach based on Green’s function for solution of fourth order BVPs: A novel fixed point approach based on Green's function for solution of fourth order BVPs

Authors: Junaid Ahmad, Muhammad Arshad

Source: Journal of Applied Mathematics and Computing. 70:2701-2719

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, numerical solution, Fixed-point theorems, boundary value problem, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, stability, Green's function, iteration

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Access URL: https://zbmath.org/7895350
https://doi.org/10.1007/s12190-024-02071-x

Advanced numerical scheme and its convergence analysis for a class of two-point singular boundary value problems

Authors: Nikhil Sriwastav, Amit K. Barnwal, Higinio Ramos, Ravi P. Agarwal, Mehakpreet Singh

Source: GREDOS. Repositorio Institucional de la Universidad de Salamanca
Universidad de Salamanca (USAL)

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Legendre wavelets, two-point singular boundary value problem, shooting-projection method, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Convergence analysis, 12 Matemáticas, Numerical methods for wavelets, Shooting-projection method, operational matrix of integration, Two-point singular boundary value problem, Operational matrix of integratio, convergence analysis

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Access URL: http://hdl.handle.net/10366/156109
https://zbmath.org/7833274
https://doi.org/10.1016/j.matcom.2023.08.037
https://hdl.handle.net/10366/156109

A new algorithm of boundary value problems based on improved wavelet basis and the reproducing kernel theory

Authors: Ruimin Zhang, Yingzhen Lin

Source: Mathematical Methods in the Applied Sciences. 47:47-57

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), BVPs, convergence, Numerical methods for wavelets, Legendre polynomials, improved wavelet orthonormal basis, stability, 0101 mathematics, Stability and convergence of numerical methods for ordinary differential equations, 01 natural sciences

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APPROXIMATION OF A FUNCTION HAVING BOUNDED DERIVATIVES UPTO THE SECOND ORDER BY SINE-COSINE WAVELET EXPANSION AND ITS APPLICATIONS: Approximation of a function having bounded derivatives upto the second order by sine-cosine wavelet expansion and its applications

Authors: Sharma, Vivek Kumar, Sharma, Virendra, Lal, Shyam, Srivastava, H. M., Rakesh

Source: Poincare Journal of Analysis and Applications. 10:193-213

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, orthonormal set, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for wavelets, Nontrigonometric harmonic analysis involving wavelets and other special systems, General harmonic expansions, frames, sine-cosine wavelet, wavelet approximation, operational matrix of integration, Numerical methods for integral equations

File Description: application/xml

Access URL: https://zbmath.org/7731237

A kernel function based regularized method for boundary value problems with noisy information

Authors: Li, X. L., Geng, F. Z., Gao, Y. Q.

Source: Applied Mathematics Letters. 164:109481

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Nonlinear boundary value problems for ordinary differential equations, noisy information, robust numerical method, boundary value problems, reproducing kernel

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Numerical and mathematical analysis of nonlocal singular Emden–Fowler type BVPs by improved Taylor-wavelet method: Numerical and mathematical analysis of nonlocal singular Emden-Fowler type BVPs by improved Taylor-wavelet method

Authors: Nikita Saha, Randhir Singh

Source: Computational and Applied Mathematics. 43

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Emden-Fowler equation, Taylor-wavelets, multi-point boundary value problems, three-point boundary value problems

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Hybrid search method for Zermelo’s navigation problem

Authors: Precioso, Daniel^{Aff1, Aff3, IDs4031402402756w_cor1}, Milson, Robert, Bu, Louis, Menchions, Yvonne, Gómez-Ullate, David

Source: Computational and Applied Mathematics. 43(4)

The nonlinear reactive transport model: An efficient approximation method based on quasilinearization and Bessel matrix method: The nonlinear reactive transport model: an efficient approximation method based on quasilinearization and Bessel matrix method

Authors: Izadi, Mohammad, Srivastava, Hari Mohan, Adel, Waleed

Source: Applied and Computational Mathematics.

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Bessel functions, Approximation by polynomials, Spectral methods applied to problems in fluid mechanics, collocation method, Nonlinear boundary value problems for ordinary differential equations, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, quasilinearization technique, convergence analysis, reactive transport model

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Higher order robust numerical computation for singularly perturbed problem involving discontinuous convective and source term

Authors: Sanjay Ku Sahoo, Vikas Gupta

Source: Mathematical Methods in the Applied Sciences. 45:4876-4898

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Finite difference and finite volume methods for ordinary differential equations, Richardson extrapolation, finite difference, convection-diffusion, discontinuous coefficients, uniform convergence, 01 natural sciences, interior layer, Mesh generation, refinement, and adaptive methods for ordinary differential equations, 0101 mathematics, Stability and convergence of numerical methods for ordinary differential equations, singular perturbation, Numerical solution of singularly perturbed problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations, piece-wise uniform mesh

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A Computational Method for Solving the Boundary Value Problem for Impulsive Systems of Essentially Loaded Differential Equations: A computational method for solving the boundary value problem for impulsive systems of essentially loaded differential equations

Authors: Kadirbayeva, Zh. M., Kabdrakhova, S. S., Mynbayeva, S. T.

Source: Lobachevskii Journal of Mathematics. 42:3675-3683

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, algorithm, Boundary value problems with impulses for ordinary differential equations, essentially loaded differential equation, Parameter dependent boundary value problems for ordinary differential equations, impulse effect, Linear boundary value problems for ordinary differential equations, 0101 mathematics, Nonlocal and multipoint boundary value problems for ordinary differential equations, parametrization method, 01 natural sciences

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A Numerical Method for Solving Boundary Value Problem for Essentially Loaded Differential Equations: A numerical method for solving boundary value problem for essentially loaded differential equations

Authors: Zh. M. Kadirbayeva

Source: Lobachevskii Journal of Mathematics. 42:551-559

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, essentially loaded differential equation, parameterization method, 0101 mathematics, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1134/S1995080221030112
https://link.springer.com/content/pdf/10.1134/S1995080221030112.pdf

A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems: A high-order numerical method for a nonlinear system of second-order boundary value problems

Authors: Minqiang Xu, Jing Niu, Li Guo

Source: Mathematical Problems in Engineering. 2020:1-7

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Nonlinear boundary value problems for ordinary differential equations, 0101 mathematics, 16. Peace & justice, 01 natural sciences

File Description: application/xml; text/xhtml

Access URL: https://downloads.hindawi.com/journals/mpe/2020/6280372.pdf
https://downloads.hindawi.com/journals/mpe/2020/6280372.pdf
http://downloads.hindawi.com/journals/mpe/2020/6280372.pdf
https://www.hindawi.com/journals/mpe/2020/6280372/

Existence results and iterative method for a fully fourth-order nonlinear integral boundary value problem

Authors: Quang A Dang, Quang Long Dang

Source: Numerical Algorithms. 85:887-907

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, iterative method, integral boundary value problem, Positive solutions to nonlinear boundary value problems for ordinary differential equations, 0101 mathematics, Nonlocal and multipoint boundary value problems for ordinary differential equations, 01 natural sciences, positivity of the solution, existence and uniqueness of the solution

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Access URL: https://dblp.uni-trier.de/db/journals/na/na85.html#DangL20
https://link.springer.com/article/10.1007/s11075-019-00842-3

A Numerical Solution for Fractional Linear Quadratic Optimal Control Problems via Shifted Legendre Polynomials: A numerical solution for fractional linear quadratic optimal control problems via shifted Legendre polynomials

Authors: Nezhadhosein, Saeed, Ghanbari, Reza, Ghorbani-Moghadam, Khatere

Source: International Journal of Applied and Computational Mathematics. 8

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, 0209 industrial biotechnology, linear qudratic time variant system, Legendre orthogonal polynomials, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, optimal control problem, Fractional ordinary differential equations, 02 engineering and technology, PDE constrained optimization (numerical aspects), fractional calculus

File Description: application/xml

Access URL: https://zbmath.org/7549898
https://doi.org/10.1007/s40819-022-01373-7