Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NUMERICAL TREATMENT OF NON-MONOTONIC BLOW-PROBLEMS BASED ON SOME NON-LOCAL TRANSFORMATIONS

  • BASEM S. ATTILI (Department of Mathematics, College of Sciences, University of Sharjah)
  • Received : 2023.01.10
  • Accepted : 2024.01.21
  • Published : 2024.03.30
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Abstract

We consider the numerical treatment of blow-up problems having non-monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non-monotonic blow-up problems, we describe and use a method of non-local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.

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References

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