Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs
This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
<p>[1] Awoyemi D.O., A Class of Continuous Method for General Second Order Initial Value Problems in Ordinary Differential Equation. J. of Computer Math, 1999; (72):29-37
[2] Onumanyi P, Awoyemi D.O, Jator S.N, and Serisena U.W, New Linear Multistep Method With Constant Coefficient for First Order Initial Value Problems J.N.M.S., 1994;13(7): 37 --51
[3] Adesanya A.O, Anake T.A, Oghoyon G.J, Continuous Implicit Method for the Solution of General Second Order Ordinary Differential Equation. J. Nigerian Association of Mathematical Physics, 2009; (40):71-78.
[4] Kayode S.J and Awoyemi D.O, A Multi derivative Collocation Method for fifth Order Ordinary Differential Equation.J. of Mathematics and Statistics. 2010; 6(1): 60-63.
[5] Milne W.E, Numerical Solution of Differential equation, Wiley Publisher, New York;1953
[6] Anake T. A, Awoyemi D. O and Adesanya A. O. One-Step Implicit Hybrid Block Method for the Direct Solution of General Second Order Ordinary Differential Equations. IAENG International Journal of Applied Mathematics, 2012;42(4):224 -228
[7] Anake T. A, Awoyemi, D. O and Adesanya A. O. One-Step Implicit Hybrid Block Method for the Direct Solution of General Second Order Ordinary Differential Equations. IAENG International Journal of Applied Mathematics, 2012: 42(4):224 -228
[8] Adesanya A Olaide, Odekunle M. Remilekun and James A. Adewale, Order seven continuous hybrid method for the solution of first order ordinary differential equations. Canadian Journal on Science and Engineering Mathematics Vol. 3 No. 4: 2012;
[9] Areo E.A, Ademiluyi R.A, and Babatola P.O, Three-step hybrid linear multistep method for the solution of first order initial value problem in ordinary differential equation ,J.N.A.M.P, 2011; (19):155-158.
[10] Yahaya Y.A. and Umar Mohammed. A family of implicit 4-step block Hybrid Collocation method for accurate and efficient solution of ODEs , Nigerian Journal of Mathematics and Applications. 2010; Vol.20: pp43-52.
[11] Sunday J. Odekunle M.R. and Adeyanya A.O. Order six block integrator for the solution of first-order ordinary differential equations, IJMSC , 2013;Vol.3 (1).1: 87-96.</p>
<p> </p>
<p>[1] Awoyemi D.O., A Class of Continuous Method for General Second Order Initial Value Problems in Ordinary Differential Equation. J. of Computer Math, 1999; (72):29-37
[2] Onumanyi P, Awoyemi D.O, Jator S.N, and Serisena U.W, New Linear Multistep Method With Constant Coefficient for First Order Initial Value Problems J.N.M.S., 1994;13(7): 37 --51
[3] Adesanya A.O, Anake T.A, Oghoyon G.J, Continuous Implicit Method for the Solution of General Second Order Ordinary Differential Equation. J. Nigerian Association of Mathematical Physics, 2009; (40):71-78.
[4] Kayode S.J and Awoyemi D.O, A Multi derivative Collocation Method for fifth Order Ordinary Differential Equation.J. of Mathematics and Statistics. 2010; 6(1): 60-63.
[5] Milne W.E, Numerical Solution of Differential equation, Wiley Publisher, New York;1953
[6] Anake T. A, Awoyemi D. O and Adesanya A. O. One-Step Implicit Hybrid Block Method for the Direct Solution of General Second Order Ordinary Differential Equations. IAENG International Journal of Applied Mathematics, 2012;42(4):224 -228
[7] Anake T. A, Awoyemi, D. O and Adesanya A. O. One-Step Implicit Hybrid Block Method for the Direct Solution of General Second Order Ordinary Differential Equations. IAENG International Journal of Applied Mathematics, 2012: 42(4):224 -228
[8] Adesanya A Olaide, Odekunle M. Remilekun and James A. Adewale, Order seven continuous hybrid method for the solution of first order ordinary differential equations. Canadian Journal on Science and Engineering Mathematics Vol. 3 No. 4: 2012;
[9] Areo E.A, Ademiluyi R.A, and Babatola P.O, Three-step hybrid linear multistep method for the solution of first order initial value problem in ordinary differential equation ,J.N.A.M.P, 2011; (19):155-158.
[10] Yahaya Y.A. and Umar Mohammed. A family of implicit 4-step block Hybrid Collocation method for accurate and efficient solution of ODEs , Nigerian Journal of Mathematics and Applications. 2010; Vol.20: pp43-52.
[11] Sunday J. Odekunle M.R. and Adeyanya A.O. Order six block integrator for the solution of first-order ordinary differential equations, IJMSC , 2013;Vol.3 (1).1: 87-96.</p>
<p> </p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65633", author = "A. A. James and A. O. Adesanya and M. R. Odekunle and D. G. Yakubu", title = "Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs", abstract = "This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
", keywords = "Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.", volume = "7", number = "11", pages = "1580-5", }
