A linear multistep method for the direct solution of initial value problems of ordinary differential equations was presented in this article. Collocation approximation method was adopted in the derivation of the scheme and then the scheme was applied as simultaneous integrator to special third order initial value problem of ordinary differential equations. The new block method possessed the desirable feature of Runge-Kutta method of being self-starting and eliminated the use of predictors. The 3-step block method is P-stable, consistent and more accurate than the existing one. Experimental results confirmed the superiority of the new scheme over the existing method.

This article presented the direct block predictor-corrector method for solving general higher order initial value problems of ordinary differential equation. Method of collocation and interpolation of power series approximate solution was used to derive a continuous linear multistep method. Block method was later used to generate the non overlapping solution at selected grid points. The method developed, is self starting, consistent, symmetric, zero-stable and convergent. The performance of the new block method was tested with some fourth order initial value problems and it was found to compare favorably with the existing methods.

Problem statement: Most important problems of medical diagnosis. When there is a cerebrovascular accident attach the chances of a successful treatment depends essentially on the early diagnosis. In practice the part of medical errors while diagnosing a stroke type comes to 20-45% even for experienced doctors and the scope of methods of neurovisualization at stroke diagnosis are limited. Approach: In this research study, attempt was made to model the application of Artificial Neural Networks to the classification of patient Cerebrovascular Accident Attack. The Network for the consisted of a three-layer feed forward artificial neural network with back-propagation error method. Results: Data were collected from 100 records of patients at Federal Medical Centre Owo, Nigeria and the Artificial Neural Networks classifier was trained using gradient decent backward propagation algorithm with flexible sigmoid activation function at one hidden layer, with 16 inputs nodes representing stroke onset symptoms at the input layer, 10 nodes at the hidden layer and one node at the output layer representing the type of the attack. Conclusion: The learning Rate γ was set between 0.1 and 0.9 while the epoch set at 150. Initial weight set at Rand (-0.5 and 0.5). The simulation results showed that the model was capable of producing a reasonable forecasting accuracy in short.

This paper proposed a new family of Non-standard finite difference schemes for the Logistic equations. The technique of non-local approximation and renormalization of the denominator function was employed. The new schemes were found to possess desirable stability properties and also preserve all the monotonic properties of the logistic equations.