{
"title": "2 \u2013 Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations",
"authors": "Abdu Masanawa Sagir",
"country": "Nigeria",
"institution": "Hassan Usman Katsina Polytechnic",
"volume": "73",
"journal": "International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering",
"pagesStart": 88,
"pagesEnd": 94,
"ISSN": "1307-6892",
"URL": "http:\/\/waset.org\/publications\/3752",
"abstract": "In this paper, linear multistep technique using power\r\nseries as the basis function is used to develop the block methods\r\nwhich are suitable for generating direct solution of the special second\r\norder ordinary differential equations of the form y\u2032\u2032 = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some\r\ngrids and off \u2013 grid points to obtain two different three discrete\r\nschemes, each of order (4,4,4)T, which were used in block form for\r\nparallel or sequential solutions of the problems. The computational\r\nburden and computer time wastage involved in the usual reduction of\r\nsecond order problem into system of first order equations are avoided\r\nby this approach. Furthermore, a stability analysis and efficiency of\r\nthe block method are tested on linear and non-linear ordinary\r\ndifferential equations whose solutions are oscillatory or nearly\r\nperiodic in nature, and the results obtained compared favourably with\r\nthe exact solution.",
"references": null,
"publisher": "World Academy of Science, Engineering and Technology",
"index": "International Science Index 73, 2013"
}