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The term "optimization" describes a way of increasing the favourable features of a function in a mathematical form while reducing the negative ones. Most of the problems encountered in the real world may be formulated as optimization problems. Particle swarm optimization is a tool which has been used extensively to handle problems across different fields. The purpose of this study is to develop a numerical method for solving nonlinear reaction-diffusion Fisher's equations, whose numerical solutions exhibit the solitons form and have a wide range of applications. This study includes differential quadrature method using exponential basis function and particle swarm optimization. In the work so far documented in the literature, a random number was used to approximate the involved parameter in the basis functions. This value is now determined using the implemented optimization technique. The numerical solutions obtained for the equation is comparable to the data available in the literature. The research presented through figures and tables, yields favourable results. [ABSTRACT FROM AUTHOR]

Describes changes required of teacher-training facilities in India, and a case for use of communication technologies to train a huge number of teachers in schools. Analyzes recent experiments in the country, as well as the effectiveness and usefulness of distance education/training. Suggests that in spite of its use in the recent past, its potentiality is yet to be fully exploited. (Author/AEF)

One of the efficient and reliable methods for resolving fractional order linear as well as non-linear differential equations is the Laplace transform with residual power series method. This approach is used in the current research to obtain the numerical solutions of the two-dimensional fractional differential equations, namely, the temporal fractional order diffusion equation and the fractional biological population equation. The unknown coefficients of the series solutions to these equations are determined using the proposed approach. The difference between exact and analytical-numerical solutions is presented for these equations in the form of errors. The advantage of the suggested method over alternative approaches is that it requires less computation to solve these two-dimensional differential equations of time-fractional order.

Present work establishes a hybrid approach called as Crank-Nicolson differential quadrature method (DQM) for evaluating the solution of the Fishers equation via utilization of modified B-spline as basis functions. The novelty of the proposed scheme is the implementation of DQM on the referred equation after the implementation of CrankNicolson scheme. The existing nonlinear terms are re-framed in a linear form via RubinGraves approach. The accuracy of the hybrid scheme is presented by the errors obtained in the numerical test problems solved numerically by the approach and hence comparing the solution with already established methods. From the presented comparisons it can be observed that the hybrid approach is providing the solutions for a relatively less number of grid points as compared to the collocation approach and produces comparable results with schemes reported in the literature. [ABSTRACT FROM AUTHOR]