http://196.220.128.81:8080/xmlui/handle/123456789/229 Wed, 20 May 2026 07:19:02 GMT 2026-05-20T07:19:02Z http://196.220.128.81:8080/xmlui/handle/123456789/5874 ONE-STEP COLLOCATION HYBRID METHOD FOR SOLVING FIST ORDER ORDINARY DIFFERENTIAL EQUATIONS EDAMISAN, AMUSEGHAN In this thesis, two one-step collocation hybrid methods for treating first order ordinary differential equation were developed. They were obtained based on continuous collocation method. The resulting methods were evaluated at some points to obtain some discrete schemes. Stability properties analysis were clone, and it showed that the methods converges (ash --. 0 and n --- x). Numerical computations were done on some sample problems on a micro-computer. The numerical results obtained demonstrate the efficiency of the method over existing methods. xii,: 76.: ill.; 32cm. Fri, 22 Apr 2005 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5874 2005-04-22T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5873 ON TWO CONTINUOUS COLLOCATION METHODS FOR SOLVING GENERAL SECOND ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS UDO, MFON OKON In this thesis two zero stable Linear Multistep methods (LMM) with continuous coetficients for solving general second order initial value problems of ordinary differential equations which does not require that the equation be reduced to a system of first order equation are considered. The approach is based on c:ollocation of the differential systems arising from the basis function at the grid points x = xn+i' 0 s i ~ k and interpolation of the approximate solution at the selected grid points x = Xn+i' for 1 < i < 3 and 2 <i <4 for the step numbers k = 3 and 4 respectively. Some predictors and their first derivatives are proposed to calculate Yn+k and Y~+k for k = 3, 4. The use of Taylor series expansion is employed for the calculation of Yn+i for i = 1,2. Evaluation of each method and its predictors at x = Xn+k gives particular discrete schemes as special cases of the methods and their predictors respectively. The new 4-step method was analysed and found to be consistent and zero stable, hence convergent. The new method was tested on some general second order initial value problems of ordinary differential equations The result showed that the method converges as h decreases. The new results were compared with the exact and the earlier result of Awoyemi (1999), it was found that the new result improved over that of Awoyerni (1999). viii.: 62p.: ill.; 32cm. Thu, 13 Apr 2006 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5873 2006-04-13T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5872 NUMERICAL TECHNIQUES FOR A VISCOUS REACTlNG FLOW IN A TUBE ALAO, Felix Ilesanmi A viscous fluid flowing through a cylinder is studied. The flow is reacting and heat is generated through reaction and viscosity. To ensure that the problem represents a physical problem we discuss the existence and uniqueness of the problem. It is shown that.the solution is unique when the parameters a and d are greater than zero and h-mesh size is such that h <: 2 .0/ (11/ a-3a (~a)% I) and h < 2.0/ (11/ d, - 3d, (~dl);'-01 ) for Equations (2.27) and (2.33). The problem has no analytical solution, hence, we investigate the problem using numerical techniques based on Shooting method and Finlte difference Scheme. The methods are compared and the best recommended based on a test solution. Finally, the effects of the parameters a,b, d., d2, d3 and viscosity on the temperature was discovered. The results show that the temperature of khe reacting system increases as the parameters a, d2 and d3 increase. On the other hand the parameters band di have opposite effects on the temperature, that is, the temperature decreases as the two parameters increase. Moreover, our numerical scheme confirmed what is physically expected the temperature increases as we increase the viscosity of the reactants. Graphs depicting the relationships between, the temperature and the parameter, and that of the temperature and the space variable feature prominently in the thesis. xi.: 86p.: ill.; 32cm. Tue, 30 Sep 1997 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5872 1997-09-30T00:00:00Z http://196.220.128.81:8080/xmlui/handle/123456789/5871 THK-ORDER INVERSE POLYNOMIAL METHODS FOR THE INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS WITH SINGULARITIES OKOSUN, KAZEEM OARE In this thesis, Inverse Polynomial Schemes are developed, analysed and computerized to solve ordinary differential equations with singularities. The method is motivated by the variety of application areas of this class of ordinary differential equations. In its development and analysis, Taylor’s series expansion, Binomial series expansion and Pade's approximation technique are used respectively, these schemes are convergent and A-Stable, Numerical results show that the schemes are effective and efficient. x.: 105p.: ill.; 32cm Mon, 17 Mar 2003 00:00:00 GMT http://196.220.128.81:8080/xmlui/handle/123456789/5871 2003-03-17T00:00:00Z