跳至主要内容

A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50198#.VDH4nFfHRK0

Author(s)   
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
Cite this paper
Badmus, A. (2014) A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations. American Journal of Computational Mathematics, 4, 376-386. doi: 10.4236/ajcm.2014.44032. 
 

[1] Yahaya, Y.A. and Badmus, A.M. (2009) A Class of Collocation Methods for General Second Order Ordinary Differential Equations. African Journal of Mathematics and Computer Science Research, 2, 69-72.
[2] Badmus, A.M. and Ekpenyong, F.E. (2013) High Order Block Method for Direct Solution of General Second Order Ordinary Differential Equations. Academy Journal of Science and Engineering, Nigerian Defence Academy Kaduna, 7, 36-42.
[3] Badmus, A.M. and Yahaya, Y.A. (2009) An Accurate Uniform Order 6 Block Method for Direct Solution of General Second Order Ordinary Differential Equations. The Pacific Journal of Science and Technology, 10, 248-254.
[4] Jator, S.N. (2007) A Class of Initial Value Methods for Direct Solution of Second Order Initial Value Problems. 4th International Conference of Applied Mathematics and Computing, Plovdiv, 12-18 August 2007.
[5] Lambert, J.D. (1973) Computational Methods in Ordinary Differential Equations. John Wiley and Sons, New York, 278.
[6] Lambert, J.D. (1991) Numerical Method for Ordinary Differential Systems. John Wiley and Sons, New York, 293.
[7] Awoyemi, D.O. (1999) A Class of Continuous Method for General Second Order IVPs in Ordinary Differential Equations. International Journal of Computer Mathematics, 72, 29-37. http://dx.doi.org/10.1080/00207169908804832
[8] Jator, S.N. (2001) Improvements in Adams-Moulton Methods for the First Initial Value Problems. Journal of the Tennessee Academy of Science, 76, 57-60.
[9] Onumanyi, P., Awoyemi, D.O., Jator, S.N. and Siriseria, U.W. (1994) New Linear Multistep Methods with Continuous Coefficients for First Order IVPs. Journal of Nigeria Mathematics Society, 13, 37-51.
[10] Awoyemi, D.O. (2003) A P-Stable Linear Multistep Method for Direct Solution of General Third Order Ordinary Differential Equation. International Journal of Computer Mathematics, 80, 987-993.
http://dx.doi.org/10.1080/0020716031000079572
[11] Vigo-Angular, J. and Ramos, H. (2006) Variable Step-Size Implementation of Multi-Step Methods . Journal of Computation and Applied Mathematics, 92, 114-131.
http://dx.doi.org/10.1016/j.cam.2005.04.043
[12] Fatunla, S.O. (1991) Block Method for Second Order Differential Equations. International Journal of Computer Mathematics, 41, 55-63. http://dx.doi.org/10.1080/00207169108804026
[13] Yahaya, Y.A. (2004) Some Theories and Applications of Continuous LMM for Ordinary Differential Equations. PhD Thesis (Unpublished), University of Jos, Nigeria.
[14] Badmus, A.M. and Mshelia, D.W. (2012) Uniform Order Zero Stable k-Step Block Methods for Initial Value Problems of Ordinary Differential Equations. Journal of Nigerian Association of Mathematical Physics, 20, 65-74.
[15] Badmus, A.M. (2014) An Efficient Seven Point Block Method for Direct Solution of General Second Order Ordinary Differential Equations . British Journal of Mathematics and Computer Science, 4, 2840-2852.
http://dx.doi.org/10.9734/BJMCS/2014/6749                  eww141006lx
标签：

评论

发表评论

此博客中的热门博文

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52202#.VIj7tMnQrzE Author(s) Stanisław Olszewski * Affiliation(s) Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland . ABSTRACT The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time. The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae. The quantization of the spin motion has been done on the basis of the old quantum theory. It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton ...
发表评论
阅读全文

Incorporation of High-Altitude Balloon Experiment in High School Science Classrooms

High-altitude balloon is a balloon, filled usually with helium or hydrogen that ascends into an area called “near space” or stratosphere. The most common type of high-altitude balloons are weather balloons. Other purposes include use as a platform for experiments in the upper atmosphere. Modern balloons generally contain electronic equipment such as radio transmitters, cameras, or satellite navigation systems, such as GPS receivers. The mission of the High-Altitude Balloon Experiment (HABE) is to acquire supporting data, validate enabling technologies, and resolve critical acquisition, tracking, and pointing (ATP) and fire control issues in support of future space-based precision pointing experiments. The use of high-altitude balloons offers a relatively low-cost, low-vibration test platform, a recoverable and reusable payload, worldwide launch capability, and a 'near- space' emulation of the future space systems operational scenarios. More recently, several university...
1 条评论
阅读全文

Fermented Brown Sugar Residue Prolongs the Caenorhabditis elegans Lifespan via DAF-16

Fermented brown sugar residue (FBSR) is generated in the course of purifying biomass ethanol from the yeast fermentation products of brown sugar. It contains abundant nutrition and is used in various industrial applications including as fertilizer and feed. Meanwhile, brown sugar has attracted attention as a health food and is thought to prevent cardiovascular diseases, hypertension, and brain stem diseases. Furthermore, polyphenol, contained in brown sugar, reduces oxidative stress and inhibits glucose absorption. DAF-16 is a transcription factor regulated downstream of the insulin signaling pathway and is one of the main factors contributing to aging and lifespan in C. elegans . Therefore, to determine the precise roles of the DAF-16 transcription factor in stress tolerance and life span, it is necessary to elucidate the signaling pathways involved in DAF-16 activation. This study was designed to elucidate the molecular mechanisms controlling the physiological stress toleran...
发表评论
阅读全文