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In this paper we attempt to revive interest in the reversion method for solving non-linear differential equations by combining the reversion technique with the Cauchy integral method for solving… (More)
Many classes of differential equation are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures.… (More)
The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential… (More)
We present an alternative approach to the discussion of Bessel equations and Bessel functions, through an elementary factorization method. The various Bessel equations are represented by a single… (More)
In seeking a generalized Rodrigues' formula solution to second-order linear ordinary differential equations a new Riccati equation is encountered and solved, leading to a novel development of the… (More)
Using a two parameter group transformation, the ordinary differential equations describing similarity solutions for the dimensionless stream function and temperature for flow over a flat plate held… (More)
The complex integral method for solving ordinary differential equations in series [3, 7, 8] is extended to cover the series solution of partial differential equations also. The means of this… (More)
New uniform approximations of the Blasius velocity profile and Blasius function are developed from existing rational approximations of the Blasius velocity profile and of the Blasius function itself.… (More)
Use is made of the existing theory of Rodrigues' formula solutions to second-order ordinary differential equations to give a brief account of the properties of relativistic Hermite polynomials.
In this paper, we derive general formulae that reproduce well-known instances of recurrence relations for the classical orthogonal polynomials as special cases. These recurrence relations are… (More)