The generalized quasilinearization technique for a second order differential equation with separated boundary conditions

Authors:
Rahmat Ali Khan
Affiliations:
Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

Citing 4
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Abstract

The method of upper and lower solutions and the method of quasilinearization for a second order nonlinear differential equation -x^''(t)=f(t,x,x^'),t@?[0,1] subject to the separated boundary conditions p"0x(0)-q"0x^'(0)=a,p"1x(1)+q"1x^'(1)=b, is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained.