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Title
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Numerical solution of the forward Kolmogorov equations in population genetics using Eta functions
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Type
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JournalPaper
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Keywords
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Population genetics, Forward Kolmogorov equations, Least squares approximation Eta functions, Error analysis, Stability
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Abstract
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This paper introduces a new numerical method for solving forward Kolmogorov equations in population genetics. Since there’s no simple analytical expression for the distribution of allele frequencies (DAF), we use these equations to derive it. The accuracy of solving these equations depends on the choice of base functions, so we use Eta-based functions for better approximations. By employing the operational matrix of integral, we simplify the partial differential equation to an algebraic one. The method’s error bounds, stability, and validity are demonstrated through numerical examples. Finally, we apply this method to analyze the behavior of forward Kolmogorov equations under various evolutionary forces.
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Researchers
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Salameh Sedaghat (Second Researcher), Somayeh Mashayekhi (First Researcher)
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