Numerical and Analitic Solution for the Integrodifferential Equation of Dna Vibrational Dynamics

We analyze the numerical and analytical of solution for the mathematical modelling of DNA vibrational dynamics with relaxing function is studied using an integrodifferential equation which takes past information from the dynamics of DNA based on the Peyrard-Bishop model for vibrational motion of DNA dynamics, some other researchers have tried from the analytical point of view. In addition, we add the boundary conditions and initial data, for that one, we consider the Sobolev spaces and some other result from the theory of functional analysis. We apply the Faedo-Galerkin method in order to obtain the required solution. Using Matlab and Fourier Series, we can obtain numerical solutions as an educational strategy for mathematical research and software development in the areas of bioinformatics.