The Application of Hybrid Methods to Solve Some Problems of Mathematical Biology |Biomedgrid

Recently, the number of papers devoted to the application of mathematical methods to solving biological problems has increased. Scientists have constructed new methods that have novel properties. As is known, a mathematical model of the problem of biology is constructed by biologists, and the solution of such models is investigated mainly by mathematicians using some mathematical constructs. As such an example, consider the problem of animal population. Given that mathematical biology emerged at the intersection of biology and mathematics, here to solve some problems of mathematical biology are invited to apply methods that are constructed at the intersection of one step and multistep methods which are called as hybrid methods. For solving these problems here are proposed stable hybrid methods with the higher order of accuracy. Here are constructed concrete stable hybrid methods with the order of accuracy and methods constructed by using linear part of the function located in the right-hand side of the differential equation, some of which are illustrated in the specific examples. It is also shown that for the stability of ecosystem, the law its conservation must obey the exponential law. To calculate the reliable values of the solution of the problem under study at the mesh points, here suggested. For this aim have constructed simple bilateral methods for solving some mathematical biological models.