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• W248457917 abstract "This paper explores the application of an Hermitian hybrid boundary integral formulation for handling Fisher-type equations. The Hermite system incorporates the problem unknowns with their space derivatives and as a consequence produces a relatively larger coefficient matrix than the corresponding linear approximation. However by adopting a finite element-like integral numerical procedure, the modified boundary integral formulation otherwise known as the Green element method (GEM) produces slender and sparse coefficient matrices which enhance an efficient solution algorithm. The resulting equations appear in the form of local elemental integral equations whose contributions add up to the coefficient matrix. This process is amply simplified in the Green element method due to the presence of the source point inside an element thereby encouraging integration to be carried out locally and accurately. This so called ‘divide and conquer’ approach is significantly much better than working with the entire matrix especially for nonlinear problems where an encounter with the problem domain can not be totally avoided. Numerical tests are carried out to illustrate the utility of this technique by comparing results obtained from both the Hermite and non-Hermite discretizations. It is observed that for each of the problems tested, not only do the results agree with those from literature, it took the Hermitian approximation fewer number of elements to achieve the same level of accuracy than its non-Hermitian version. However, application of same technique to multi-dimensional problems may not be as straightforward due to the construction and storing of the Hermite system matrix which will not only involve non-trivial operations in terms of a high computational cost but also a compromise in the quality of the numerical solution arising from significant round-off errors." @default.
• W248457917 created "2016-06-24" @default.
• W248457917 creator A5033894365 @default.
• W248457917 date "2015-01-01" @default.
• W248457917 modified "2023-09-26" @default.
• W248457917 title "An Hermitian Boundary Integral Hybrid Formulation for Nonlinear Fisher-Type Equations" @default.
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• W248457917 doi "https://doi.org/10.11648/j.acm.20150403.11" @default.
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