On the Performance of Haar Wavelet Approach for Boundary Value Problems and Systems of Fredholm Integral Equations
I. K. Youssef,
R. A. Ibrahim
Issue:
Volume 2, Issue 4, July 2017
Pages:
39-46
Received:
31 May 2017
Accepted:
13 June 2017
Published:
17 July 2017
Abstract: The Haar wavelet method applied to different kinds of integral equations (Fredholm integral equation, integro-differential equations and system of linear Fredholm integral equations) and boundary value problems (BVP) representation of integral equations. Three test problems whose exact solutions are known were considered to measure the performance of Haar wavelet. The calculations show that solving the problem as integral equation is more accurate than solving it as differential equation. Also the calculations show the efficiency of Haar wavelet in case of F. I. E. S and integro-differential equations comparing with other methods, especially when we increase the number of collocation points. All calculations are done by the Computer Algebra Facilities included in Mathematica 10.2.
Abstract: The Haar wavelet method applied to different kinds of integral equations (Fredholm integral equation, integro-differential equations and system of linear Fredholm integral equations) and boundary value problems (BVP) representation of integral equations. Three test problems whose exact solutions are known were considered to measure the performance ...
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On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems
Mohamed Seddeek,
Sayeda Nabhan Odda
Issue:
Volume 2, Issue 4, July 2017
Pages:
47-50
Received:
11 May 2017
Accepted:
6 June 2017
Published:
31 July 2017
Abstract: We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.
Abstract: We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher or...
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