scholarly journals Bernoulli polynomial and the numerical solution of high-order boundary value problems

2019 ◽  
Vol 04 (01) ◽  
pp. 45-59 ◽  
Author(s):  
Mohamed El-Gamel ◽  
Waleed Adel ◽  
M. S. El-Azab
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Bernoulli Polynomial ◽  
High Order

scholarly journals A new method for high-order boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yingchao Zhang ◽  
Liangcai Mei ◽  
Yingzhen Lin
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Algorithm ◽  
Time Complexity ◽  
Numerical Experiments ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
High Order

AbstractThis paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in $W^{m}_{2}[0,1]$ W 2 m [ 0 , 1 ] . Based on the orthonormal basis, the numerical solution of the boundary value problem is obtained by finding the ε-approximate solution. In addition, the convergence order, stability, and time complexity of the method are discussed theoretically. At last, several numerical experiments show the feasibility of the proposed method.

scholarly journals Numerical Solution of High Order Bernoulli Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Costabile ◽  
A. Napoli
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
General Procedure ◽  
Boundary Value ◽  
Recurrence Formula ◽  
High Order ◽  
Collocation Methods ◽  
Special Boundary ◽  
Numerical Examples ◽  
Practical Usefulness

For the numerical solution of high order boundary value problems with special boundary conditions a general procedure to determine collocation methods is derived and studied. Computation of the integrals which appear in the coefficients is generated by a recurrence formula and no integrals are involved in the calculation. Several numerical examples are presented to demonstrate the practical usefulness of the proposed method.

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