This paper deals with the construction of piecewise analytic approximate solutions for nonlinear initial value problems modeled by a system of nonlinear ordinary differential equations. In real world several biological and environmental parameters in the predator-prey model vary in time. Thus, non-autonomous systems are important to be studied. We show the effectiveness of the method for autono...

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performe...

occur in the analysis of biological networks. They also include as special cases the known growth laws and probability functions, famous differential equations like those of Bessel, Chebyshev, and Laguerre, and solutions to important physical problems. These systems have no known analytical solution. However, an important subclass comprising many of the special cases mentioned above is solved. ...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.