scholarly journals Direct Computation of Operational Matrices for Polynomial Bases

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Osvaldo Guimarães ◽  
José Roberto C. Piqueira ◽  
Marcio Lobo Netto
Keyword(s):  
Hilbert Space ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Operational Matrices ◽  
Direct Computation ◽  
Linear Operation ◽  
Matrix Operations ◽  
Polynomial Bases ◽  
Reference Matrix

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

scholarly journals Reproducing kernel functions for linear tenth-order boundary value problems

2018 ◽  
Vol 22 ◽  
pp. 01027
Author(s):  
Ali Akgül ◽  
Esra Karatas Akgül ◽  
Baris Orcan ◽  
Mustafa Inc
Keyword(s):  
Hilbert Space ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Kernel Functions ◽  
Space Method ◽  
Higher Order Differential Equations

Higher order differential equations have always been an onerous problem to investigate for the mathematicians and engineers. Different numerical methods were applied to get numerical approximations of such problems. This paper gives some reproducing kernel functions to find approximate solutions of the tenth-order boundary value problems (BVPs). These reproducing kernel functions are very important in the reproducing kernel Hilbert space method.

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