Abstract
A localized radial basis function meshless method is applied to approximate a nonlinear biological population model with highly satisfactory results. The method approximates the derivatives at every point corresponding to their local support domain. The method is well suited for arbitrary domains. Compared to the finite element and element free Galerkin methods, no integration tool is required. Four examples are demonstrated to check the efficiency and accuracy of the method. The results are compared with an exact solution and other methods available in literature.
Highlights
Biological population models have attracted many researchers in the last few years
The equation describes that rate of population directly supplied to R is equal to the sum of the rate of change of population and the rate at which individuals leave R across the boundary [1,2,3]
To overcome the problems occurring during global radial basis function (RBF), partition of unity, domain decomposition method and greedy algorithms have been discovered [26,27,28]
Summary
Biological population models have attracted many researchers in the last few years. Consider the nonlinear biological population model [1]. Meshless procedures have attracted researchers because they can be applied to a complex shaped domain with high dimensional problems These methods include the radial basis function (RBF) [7,8,9], smooth particle hydrodynamics methods (SPH) [10], reproducing kernel particle method (RKPM) [11], element free Galerkin method (EFG) [11], and meshless local Petrov Galerkin method (MLPG) [12]. To overcome the problems occurring during global RBFs, partition of unity, domain decomposition method and greedy algorithms have been discovered [26,27,28] Another alternative is the implementation of local RBFs (LRBFs) [29,30,31]. We have applied local RBFs to solve the nonlinear biological model
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