The 7 and 8 Families of Hybrid Block Methods for Numerical Solution of Initial Value Problems in Stiff Equations

2017 ◽  
Vol 23 (1) ◽  
pp. 1-11
Author(s):  
Y Skwame
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Initial Value ◽  
Stiff Equations ◽  
Block Methods

scholarly journals Direct Solution of Second Order Ordinary Differential Equations Using a Class of Hybrid Block Methods

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Emmanuel A Areo ◽  
Nosimot O Adeyanju ◽  
Sunday J Kayode
Keyword(s):  
Initial Value Problems ◽  
Hybrid Methods ◽  
Multistep Method ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
Order Error ◽  
Block Methods ◽  
Grid Points ◽  
Step Number

This research proposes the derivation of a class of hybrid methods for solution of second order initial value problems (IVPs) in block mode. Continuous linear multistep method of two cases with step number k = 4 is developed by interpolating the basis function at certain grid points and collocating the differential system at both grid and off-grid points. The basic properties of the method including order, error constant, zero stability, consistency and convergence were investigated. In order to examine the accuracy of the methods, some differential problems of order two were solved and results generated show a better performance when comparison is made with some current methods.Keywords- Block Method, Hybrid Points, Initial Value Problems, Power Series, Second Order 

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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