An innovative harmonic numbers operational matrix method for solving initial value problems

CALCOLO ◽  
2016 ◽  
Vol 54 (1) ◽  
pp. 57-76 ◽  
Author(s):  
Anna Napoli ◽  
W. M. Abd-Elhameed
Keyword(s):  
Matrix Method ◽  
Initial Value Problems ◽  
Operational Matrix ◽  
Harmonic Numbers ◽  
Initial Value ◽  
Operational Matrix Method

scholarly journals Chebyshev Operational Matrix Method for Lane-Emden Problem

2019 ◽  
Vol 8 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Bhuvnesh Sharma ◽  
Sunil Kumar ◽  
M.K. Paswan ◽  
Dindayal Mahato
Keyword(s):  
Chebyshev Polynomial ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Absolute Error ◽  
Initial Value ◽  
Operational Matrix Method ◽  
Modified Method ◽  
Operational Matrix Of Differentiation ◽  
Linear And Nonlinear

AbstractIn the this paper, a new modified method is proposed for solving linear and nonlinear Lane-Emden type equations using first kind Chebyshev operational matrix of differentiation. The properties of first kind Chebyshev polynomial and their shifted polynomial are first presented. These properties together with the operation matrix of differentiation of first kind Chebyshev polynomial are utilized to obtain numerical solutions of a class of linear and nonlinear LaneEmden type singular initial value problems (IVPs). The absolute error of this method is graphically presented. The proposed framework is different from other numerical methods and can be used in differential equations of the same type. Several examples are illuminated to reveal the accuracy and validity of the proposed method.

scholarly journals A Reliable Method for Solving Fractional Sturm–Liouville Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 176 ◽  
Author(s):  
M. Khashshan ◽  
Muhammed Syam ◽  
Ahlam Al Mokhmari
Keyword(s):  
Matrix Method ◽  
Reliable Method ◽  
Operational Matrix ◽  
Liouville Problem ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Sturm Liouville

In this paper, a reliable method for solving fractional Sturm–Liouville problem based on the operational matrix method is presented. Some of our numerical examples are presented.

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