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Many undergraduate courses in mathematics contain an introduction to the numerical methods for ordinary differential equations (ODEs). Numerical methods that have been conventionally applied in solving the initial value problem (IVP) of first order ODEs are from the class of linear multistep method (LMM) and Runge-Kutta method (RKM), which are derived based on polynomial functions. However, the conventional methods are found to be inefficient in solving problems with special characteristic which are singular, stiffness and singular perturbation. This book focuses on developing numerical approaches from the class of rational methods of second, third and fourth order of accuracy, and the schemes are derived based on the rational functions with denominator of degree one.


Instructor Biography

Dr. Zanariah Abdul Majid received her BA in Mathematics from Macalaster College, Minnesota, USA in 1986, MA in Mathematics from Eastern Michigan University, USA in 1988, Diploma Education in Mathematics from Universiti Kebangsaan Malaysia in 1990 and PhD in Applied Mathematics from Universiti Putra Malaysia in 2004. She began her teaching career in 1990 as a teacher in secondary school. Six years later, she joined the Teacher’s Training College as a lecturer in Department of Mathematics. She has retired as academic lecturer and currently as Amal Putra at Faculty Science, Universiti Putra Malaysia. She is a life member of the Malaysian Mathematical Sciences Society. She won several awards and gold medals with her hard work and distinguished efforts in research at international and national level. She has published more than 150 papers in the area of numerical analysis. Her research interest focus on multistep method and one-step method for solving higher order ordinary differential equations, boundary value problem, delay differential equations, volterra-integro differential equations, fredholm-integro differential equations and fuzzy differential equations.

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