scholarly journals A new stepsize change technique for Adams methods

2016 ◽  
Vol 1 (2) ◽  
pp. 547-558 ◽  
Author(s):  
M. Calvo ◽  
J.I. Montijano ◽  
L. Rández
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Error Term ◽  
Computational Cost ◽  
New Technique ◽  
Initial Value ◽  
Change Technique ◽  
Adams Methods ◽  
Interpolation Technique ◽  
A New Technique

AbstractIn this paper a new technique for stepsize changing in the numerical solution of Initial Value Problems for ODEs by means of Adams type methods is considered. The computational cost of the new technique is equivalent to those of the well known interpolation technique (IT). It is seen that the new technique has better stability properties than the IT and moreover, its leading error term is smaller. These facts imply that the new technique can outperform the IT.

scholarly journals A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

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