An effective approximation for singularly perturbed problem with multi-point boundary value - Arslan, Derya (New trends in mathematical sciences, 2021)
According to some references, existence and uniqueness of nonlocal problems can be seen in [1,4,22]. [...]We formulate the iterative algorithm for solving the discrete problem and a numerical example present to find the solution of approximation in Section 5. [...]we will integrate the Equation (1) over (x,_i,xi+i), here {(?i{x)}=i is the basis functions that {(Pi{x)}=i has the following form where ji = y -f', <P; (x) and '(x), respectively, are the solution of the problems as: [...]the following uniform error estimate satisfies 5 Algorithm and numerical results Here an effective algorithm has been given for the solution of the difference scheme (16)-(18) and numerical results have also been displayed in table and graphs. (a) We give the algorithm for the solution of the difference scheme (16)-(18): (b) We examine the following problem to see how the method works: where We have the exact solution of this problem as The corresponding e- uniform convergence rates are computed using the formula The error estimates are denoted by 6 Conclusion In this study, we have offered an effective finite difference method for solving second-order linear singularly perturbed multi-point boundary value problem.