A Higher Order Implicit Method for Numerical Solution of Singular Initial Value Problems

2017 ◽  
pp. 255-264 ◽  
Author(s):  
M. Kamrul Hasan ◽  
M. Suzan Ahamed ◽  
B. M. Ikramul Haque ◽  
M. S. Alam ◽  
M. Bellal Hossain
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Higher Order ◽  
Implicit Method ◽  
Initial Value

scholarly journals Implicit Methods for Numerical Solution of Singular Initial Value Problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Md. Rahaman Habibur ◽  
M. Kamrul Hasan ◽  
Md. Ayub Ali ◽  
M. Shamsul Alam
Keyword(s):  
Singular Point ◽  
Numerical Solution ◽  
Initial Value Problems ◽  
Accurate Result ◽  
Implicit Method ◽  
Implicit Methods ◽  
Initial Value ◽  
Runge Kutta

AbstractVarious order of implicit method has been formulated for solving initial value problems having an initial singular point. The method provides better result than those obtained by used implicit formulae developed based on Euler and Runge-Kutta methods. Romberg scheme has been used for obtaining more accurate result.

scholarly journals An Implicit Method for Numerical Solution of Second Order Singular Initial Value Problems

2014 ◽  
Vol 7 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Mohammad Kamrul Hasan ◽  
Mohammad Suzan Ahamed ◽  
Mohammad Ashraful Huq ◽  
Mohammad Shamsul Alam ◽  
Mohammad Bellal Hossain
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Second Order ◽  
Implicit Method ◽  
Initial Value

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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