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Theorems and Lemmas without Proofs: Theorems 2. Lemmas 2. These topic can be found in the and fourth chapters of the recommended book sections The students should study the following topics: Chapter 2: Solution of Nonlinear Equations The bisection method: How to apply it and to compute an error bound for the approximate solutions derived by the method. The Newtons method: How to apply it and the analysis of its error. The secant method: How to apply it. The fixed point iterative method: How to formulate the function g x which will satises the conditions of the Theorem 2.
Butt; Finite element approximation for variational inequalities, Punjab J. Butt; Some aspects of elliptic variational inequalities, Korean J.
Butt; Some aspects of optimal shape design problems,J. Volume 59, No. Butt; Numerical Solution of variational inequalities, Punjab J.
Butt; Domain variational formulation for free boundary value problem, Punjab J. Butt; An Optimization problem described by a fourth-order variational inequalities, J.
Butt; Implementation of some methods of shape design for a fourth-order variational inequalities, J. Butt; An existence theory of a fourth-order variational inequality by a penalty method Accepted , Applied Mathematical Sciences, Butt; Local convergence and optimal shape design, Indian J.
Pure Appl. Skip to main content. Applied Linear Algebra - Math Integral Calculus - Math Numerical Methods- Math Publications An Optimization problem described by a fourth-order variational i Upcoming SlideShare.
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No Downloads. Views Total views. Actions Shares. Embeds 0 No embeds. No notes for slide. Rounding off Errors in Addition and Subtraction It describes how addition and subtraction of numbers are performed in a computer.
Rounding off Errors in Multiplication It describes how multiplication of numbers are performed in a computer. Rounding off Errors in Division It describes how division of numbers are performed in a computer.
Rounding off Errors in Powers and roots It describes how the powers and roots of numbers are performed in a computer. Method of Bisection This is simple and slow convergence method but convergence is guaranteed and is based on the Intermediate Value Theorem.
Its strategy is to bisect the interval from one endpoint of the interval to the other endpoint and then retain the half interval whose end still bracket the root. False Position Method This is slow convergence method and may be thought of as an attempt to improve the convergence characteristic of bisection method. Its also known as the method of linear interpolation. Fixed-Point Method This is very general method for finding the root of nonlinear equation and provides us with a theoretical framework within which the convergence properties of subsequent methods can be evaluated.