Analytical-numerical solution of coupled singular mixed diffusion type problems

ANALYTICAL-NUMERICAL SOLUTION FOR NONLINEAR INTEGRAL EQUATIONS OF HAMMERSTEIN TYPE

Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...

Analytical and numerical solution of coupled KdV - MKdV system

The matrix 2x2 spectral differential equation of the second order is considered on x in (−∞, +∞). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second covariant equation to form Lax pair of a coupled KdV-MKdV system. The sequence of the elementary Darboux transformations of the zero-potential seed produce two-parameter soluti...

An Approximate Analytical Solution of Coupled Nonlinear Fractional Diffusion Equations

In recent years, fractional reaction-diffusion models have been studied due to their usefulness and importance in many areas of mathematics, statistics, physics, and chemistry. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative. The resulting solutions spread faster than classical solutions and may exhibit asymmetry, dependin...

Analytic-numerical solutions of mixed problems for coupled systems of generalized diffusion equations with delay

REFERENCES [1] Wu, J. Theory and Application of Partial Functional Differential Equations. Springer Verlag, New York, 1996. [2] Martín, J.A., Rodríguez, F., Company, R. Analytical solution of mixed problems for the generalized diffusion equation with delay. Mathematical and Computer Modelling, 40 (2004), 361--369. [3] Reyes, E., Rodríguez, F., Martín, J.A. Cálculo eficiente de soluciones numéri...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions