Document Type : Research Paper


School of Physical and Applied Science, Kenyatta University P.O BOX 43844-0010, Nairobi, Kenya


n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 


[1] Adomian G.,” Solving Frontier Problems on physics, the decomposition method”.Kluwer Academic Publisher, Boston, 1994.
[2] Carroll R.,” Some Singular Cauchy Problems”, Ann.Mat.Pura Appl., 56, 1-31, 1951.
[3] Carroll R., and Showalter R.,” Singular and Degenerate Cauchy Problems”. Academic Press, New York, Vol.127-p 333, 1976.
[4] Euler L.,” Institiones Calculi Integralis, III”. Petroli, 1770.
[5] Weinstein A., ”Sur le Proble’me de Cauchy pour1’ e’quation de poisson et 1’equationdes ondes.” Critical review, Paris, 234,2584-2585, 1952.
[6] Weinstein A.,” On the wave equation and the equation of Euler-Poisson-Darboux” Proceedings of the 5th symp.App.Math;Amer.Math.Soc. McGraw-Hill,  New, 1954.