Relevant bibliographies by topics / Numerical blow-up

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Numerical blow-up'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Numerical blow-up"

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Cho, Chien-Hong, and Ying-Jung Lu. "On the numerical solutions for a parabolic system with blow-up." AIMS Mathematics 6, no. 11 (2021): 11749–77. http://dx.doi.org/10.3934/math.2021683.

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<abstract><p>We study the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. A scheme with adaptive temporal increments is commonly used to compute an approximate blow-up time. There are, however, some limitations to reproduce the blow-up behaviors for such schemes. We thus use an algorithm, in which uniform temporal grids are used, for the computation of the blow-up time and blow-up behaviors. In addition to the convergence of the numerical blow-up time, we also study various blow-up behaviors numerically, including the blow-up set, blow
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Maan, A. Rasheed, and Farhan A.G. "On Blow-up Time and Rate Of The Numerical Solutions of The Semilinear Heat Equation with Reaction Term." Journal of Progressive Research in Mathematics 9, no. 1 (2016): 1333–40. https://doi.org/10.5281/zenodo.3976761.

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In this paper, we study the numerical blow-up solutions and times of the semilinear heat equation with reaction term. We compute the blow-up growth rate in the numerical solutions of two numerical experiments, depending on the blow-up solutions and times, those have been computed using a finite difference method.
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Fernández Bonder, Julián, Pablo Groisman, and Julio D. Rossi. "On numerical blow-up sets." Proceedings of the American Mathematical Society 130, no. 7 (2002): 2049–55. http://dx.doi.org/10.1090/s0002-9939-02-06350-5.

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Cho, Chien-Hong. "Numerical detection of blow-up: a new sufficient condition for blow-up." Japan Journal of Industrial and Applied Mathematics 33, no. 1 (2015): 81–98. http://dx.doi.org/10.1007/s13160-015-0198-0.

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FERREIRA, RAÚL, PABLO GROISMAN, and JULIO D. ROSSI. "NUMERICAL BLOW-UP FOR A NONLINEAR PROBLEM WITH A NONLINEAR BOUNDARY CONDITION." Mathematical Models and Methods in Applied Sciences 12, no. 04 (2002): 461–83. http://dx.doi.org/10.1142/s021820250200174x.

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In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.
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Khalil, Manar, Ishak Hashim, Maan Rasheed, Faieza Samat, and Shaher Momani. "Numerical Finite-Difference Approximations of a Coupled Reaction-Diffusion System with Gradient Terms." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1516–38. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5246.

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This study focuses on the derivation of explicit and implicit finite difference formulas.The objective of this study is to derive an estimation of the blow-up time for a coupled reaction-diffusion system incorporating gradient terms, employing numerical finite difference approximations. Furthermore, an examination is conducted on the consistency, stability, and convergence of the proposed schemes. Additionally, the study presents two numerical experiments. In each instance, the numerical blow-up time is calculated benefit the suggested methodologies, employing varying space steps and non-fixed
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Lekporo, K. Z., K. B. Edja,, N. Koffi, and K. A. Touré. "SIMULTANEOUS NUMERICAL BLOW-UP IN A FOUR-COMPONENT SYSTEM OF HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS." Advances in Mathematics: Scientific Journal 14, no. 2 (2025): 157–86. https://doi.org/10.37418/amsj.14.2.3.

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This paper investigates the numerical approximation of a system of heat equations with nonlinear boundary conditions. We prove that the solution of a semidiscrete form of above problem blows up in a finite time. We also establish certain conditions under which simultaneous blow-up occurs for the solution of the semidiscrete problem. After showing that the numerical blow-up time converges to the theoretical blow-up time as the mesh size tends to zero, we finally present some numerical results to illustrate key points of our work.
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Chung, Soon-Yeong, and Jae-Hwang Lee. "Blow-up for discrete reaction-diffusion equations on networks." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 103–19. http://dx.doi.org/10.2298/aadm150210005c.

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In this paper, we discuss the conditions under which blow-up occurs for the solutions of reaction-diffusion equations on networks. The analysis of this class of problems includes the existence of blow-up in finite time and the determination of the blow-up time and the corresponding blow-up rate. In addition, when the solution blows up, we give estimates for the blow-up time and also provide the blow-up rate. Finally, we show some numerical illustrations which describe the main results.
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Ferreira, Raŭl, and Arturo De Pablo. "Numerical Blow-up for the p-Aplacian Equation with a Source." Computational Methods in Applied Mathematics 5, no. 2 (2005): 137–54. http://dx.doi.org/10.2478/cmam-2005-0007.

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AbstractWe study numerical approximations of nonnegative solutions of the p-Laplacian equation with a nonlinear source. We describe when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow-up rates and the blow-up sets by means of the discrete self-similar profiles.
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Stuart, A. M., and M. S. Floater. "On the computation of blow-up." European Journal of Applied Mathematics 1, no. 1 (1990): 47–71. http://dx.doi.org/10.1017/s095679250000005x.

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Numerical methods for initial-value problems which develop singularities in finite time are analyzed. The objective is to determine simple strategies which produce the correct asymptotic behaviour and give an accurate approximation of the blow-up time. Fixed step methods for scalar ordinary differential equations are studied first and it is shown that there is a natural embedding of the discrete process in a continuous one. This shows clearly how and why the fixed-step strategy fails. A class of time-stepping strategies that correspond to a time- continuous re-scaling of the underlying differe
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Dissertations / Theses on the topic "Numerical blow-up"

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Wu, Yi-Chien, and 吳依蒨. "Numerical Blow-up Problems for a Convective Reaction-diffusion Equation." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/24834213527151025431.

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碩士<br>國立中正大學<br>數學研究所<br>102<br>We consider a finite difference scheme for the convective reaction-diffusion equation $u_t=u_{xx}+\alpha(u^m)_x+u^{\beta}, (0< x< 1,~ 0<t)$, where $\beta>m\geqslant 1$ and $\alpha>0$ are parameters. For many differential equations or systems the solutions can become unbounded in finite time $T$. Here the phenomena that is known as blow-up and the finite time $T$ is called the blow-up time. In this paper, we prove that the numerical blow-up time converges to the blow-up time with uniform temporal grid size.
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Bruso, Keith Alvin. "Existence, uniqueness and blow-up results for non-linear wave equations." 1985. http://hdl.handle.net/2097/27403.

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Hu, Chang-Wei, and 胡昶偉. "On the Numerical Blow-up Set for the Semilinear Heat Equation." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/62799852668203467490.

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碩士<br>國立中正大學<br>數學研究所<br>102<br>We consider the finite difference approximation for the semilinear heat equation u_t = u_xx+f(u) (0 < t; 0 < x < 1) with nonnegative initial data u(0, x) = u_0(x) (0 < x < 1) and the Dirichlet boundary condition u(t, 0) = u(t, 1) = 0 (t > 0). It is known that although the finite-time blow-up for the semilinear heat equation can be reproduced by a scheme with adaptively-defined time mesh, the numerical blow-up sets do not always coincide with that of the real one. In this paper, we are aimed to investigate the numerical blow-up sets with respect to different time
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LIN, SHU-XUAN, and 林紓瑄. "Numerical blow-up behavior for axisymmetric solutions of semilinear heat equation." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/e9a8xu.

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Chen, Ke-Ming, and 陳克鳴. "On the Numerical Blow-up Set for the Semi-linear Heat Equation." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/86620925437710064503.

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碩士<br>國立中正大學<br>應用數學研究所<br>99<br>We consider the semi-linear parabolic blow-up problem u_t=u_{xx}+f(u) (0<x<1, t>0) with certain choices of f and their finite difference analogues whose solutions also blow up in finite time. In this paper, we are going to classify the exact numerical blow-up sets. It is interesting that despite of the convergence of the numerical solutions and the numerical blow-up time, the numerical blow-up sets do not always coincide with that of the PDE. However, the blow-up shapes seem to be realized by our difference schemes.
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DU, BI-YI, and 杜碧怡. "Convergence for the numerical blow up time of a nonlinear ODE problem." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/php9kh.

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碩士<br>國立中正大學<br>數學系應用數學研究所<br>106<br>We consider the frst order nonlinear ODE blow-up problem u′(t)=G(u). Nakagawa [6] proposed a scheme with adaptively-defned temporal increment for the computation of the blow-up solutions. Later, an algorithm using uniform time mesh was proposed by Cho [3] for the computation of the numerical blow-up time. Nevertheless, these schemes are of order 1 in time variable so that the convergence order of the numerical blow-up time is also of order 1. In this presentation, we would like to consider a question as to can we have a higher convergence order if we use a
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Dlamini, Phumlani Goodwill. "Numerical simulation of finite-time blow-up in nonlinear ODEs, reaction-diffusion equations and VIDEs." Thesis, 2012. http://hdl.handle.net/10210/8054.

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M.Sc.<br>There have been an extensive study on solutions of differential equations modeling physical phenomena that blows up in finite time. The blow-up time often represents an important change in the properties of such models and hence it is very important to compute it as accurate as possible. In this work, an adaptive in time numerical method for computing blow-up solutions for nonlinear ODEs is introduced. The method is named implicit midpoint-implicit Euler method (IMIE) and is based on the implicit Euler and the implicit midpoint method. The method is used to compute blow-up time for di
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LUO, YI-XUAN, and 羅易宣. "Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/383xuy.

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碩士<br>國立中正大學<br>數學系應用數學研究所<br>105<br>This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove that our numerical solutions converge to the exact solution and that the numerical blow-up time also converges to the exact blow-up time. Several numerical examples concerning the blow-up behavior of odd p and the special case p=2 are also reported.
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Book chapters on the topic "Numerical blow-up"

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Lukyanenko, Dmitry, and Nikolay Nefedov. "Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification: Asymptotics and Numerical Diagnostics." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_7.

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Rozanova, Olga S. "Blow-up of Solutions in System of Atmosphere Dynamics." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8724-3_30.

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"Numerical blow-up time." In Exact Finite-Difference Schemes. De Gruyter, 2016. http://dx.doi.org/10.1515/9783110491326-009.

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"Chapter 6 Numerical methods of solution of initial-boundary-value problems for Sobolev-type equations." In Blow-up in Nonlinear Sobolev Type Equations. De Gruyter, 2011. http://dx.doi.org/10.1515/9783110255294.543.

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Abia, L. M., J. C. López-Marcos, and Julia Martínez. "Numerical blow-up time convergence for discretizations of reaction-diffusion equations." In Equadiff 99. World Scientific Publishing Company, 2000. http://dx.doi.org/10.1142/9789812792617_0210.

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"Asymptotic Behavior of Blow-Up Solutions of the Nonlinear Schrodinger Equation with Critical Power Nonlinearity." In Proceedings of the Second International Colloquium on Numerical Analysis. De Gruyter, 1994. http://dx.doi.org/10.1515/9783112318805-015.

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I. Semenov, Vladimir. "About Bellman Principle and Solution Properties for Navier–Stokes Equations in the 3D Cauchy Problem." In Vortex Dynamics - Theoretical, Experimental and Numerical Approaches [Working Title]. IntechOpen, 2024. http://dx.doi.org/10.5772/intechopen.1005758.

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Without belittling the achievements of many mathematicians in the studying of the Navier-Stokes equations, the real ways opened J. Leray and O.A. Ladyzhenskaya. The main goal of this work is to compare the smoothness property of a weak solution in the Cauchy problem after some moment if it is known solution regularity until this moment with the optimality property in the Bellman principle. Naturally, all these are connected with the existence problem of blow up solution in the Cauchy problem for Navier-Stokes equations in space attracting a lot of attention up to now. The smoothness control an
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Conference papers on the topic "Numerical blow-up"

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Zhengqiu, Ling, and Qin Siqian. "Blow-up analysis of a parabolic system." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027649.

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Nipp, Kaspar, Daniel Stoffer, Peter Szmolyan, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Graph Transform and Blow-up in Singular Perturbations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241616.

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Belov, A. A., and M. O. Korpusov. "Numerical blow-up diagnostics for differential equation solutions." In 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS). IEEE, 2017. http://dx.doi.org/10.1109/piers.2017.8262198.

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Galakhov, E., and O. Salieva. "On blow-up for a generalized heat inequality." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912964.

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Scheichl, Stefan, and Stefan Braun. "On blow-up solutions in marginally separated triple-deck flows." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825477.

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Willie, Robert. "AKS-chemotaxis model generalized well-posedness, blow-up dynamics and controllability." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044155.

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LIANG, K. W., P. LIN, and R. C. E. TAN. "Numerical Solution of Blow-Up Problems Using Mesh-Dependent Variable Temporal Steps." In Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC) 2002. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2002. http://dx.doi.org/10.1142/9781860949524_0164.

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Fan, Enyu, and Changpin Li. "Numerical simulation of blow-up solution to the Caputo-Hadamard fractional differential equation." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153168.

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Deviaterikova, E., E. Galakhov, O. Salieva, and L. Uvarova. "Blow-up time for a problem of heat transfer with coefficients depending on their formation mechanisms." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912963.

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Kutev, N., N. Kolkovska, M. Dimova, C. I. Christov, Michail D. Todorov, and Christo I. Christov. "Theoretical and Numerical Aspects for Global Existence and Blow Up for the Solutions to Boussinesq Paradigm Equation." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 3rd International Conference—AMiTaNS'11. AIP, 2011. http://dx.doi.org/10.1063/1.3659905.

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