Research Article

An Efficient and Straightforward Numerical Technique Coupled to Classical Newton’s Method for Enhancing the Accuracy of Approximate Solutions Associated with Scalar Nonlinear Equations

Table 1

Approximate solution of scalar nonlinear equation (when guest point = 3) obtained by Classical Newton’s Method (CNM) (cf. Section 2.2), Classical Newton’s Method coupled with New Numerical Technique (CNM + NNT) for conditions [A1] and [A2] (cf. Section 2.3), and Third-order Modified Newton’s Method (TMNM) (cf. Section 3.1). Notations: () (resp., ()) denotes that approximate solution is provided using (21a) (resp., (21b)) in Section 2.3.1.

Iteration ()CNMCNM + NNT with condition [A1]CNM + NNT with condition [A2]TMNM

03.00000000003.00000000003.00000000003.0000000000
12.24714263051.4942904056 ()1.4942904056 ()1.9644439737
21.68238265931.1286469200 ()0.7631581663 ()1.2884809024
31.23373883020.8906377962 ()0.7721173336 ()0.8906149334
40.97232002290.7878458749 ()0.7720250356 ()0.7746164630
50.81467075200.7723183427 ()0.7720250256 ()0.7720250503
60.77414308510.7720251266 ()0.7720250256
70.77203029090.7720250256 ()
80.7720250256
90.7720250256
10