A PICARD-S HYBRID TYPE ITERATION METHOD FOR SOLVING A DIFFERENTIAL EQUATION WITH RETARDED ARGUMENT

By Faik Gursoy, Vatan Karakaya. 2014

109 citations recorded by the source corpus.

We introduce a new iteration method what is called Picard-S itera- tion. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and converges faster than CR iteration method for the aforementioned class of mappings. Furthermore, by providing an example, it is shown that the Picard-S iteration method converges faster than all of Picard, Mann, Ishikawa, Noor, SP, CR, S and some other iteration methods in the existing literature when applied to contraction mappings. A data dependence result is proven for fixed point of contraction mappings with help of the new iteration method. Finally, we show that the Picard-S iteration method can be used to solve differential equations with retarded argument.

Subfields: Geometry and Topology, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7b7a45b7e798b47bc284fa6bd4e84c187f302bb2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Muhammad Arshad
2. Kifayat Ullah
3. Vatan Karakaya

In Modeling and Simulation

1. Muhammad Arshad
2. Kifayat Ullah

In Numerical Analysis

1. Muhammad Arshad
2. Kifayat Ullah
3. Vatan Karakaya

Citations in the corpus

• SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION PROCESS IN BANACH SPACES (2017, result): “We will follow the same scheme of proof as for a similar result on overlaps ([8], Theorem 1).”
• Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process (2018, methodology): “We can easily see that the new M iterations are the first converging one than the S iterations and the Picard-S iterations.”