Computer Oriented Numerical Scheme for Solving Engineering Problems

Shams, Mudassir; Rafiq, Naila; Kausar, Nasreen; Mir, Nazir Ahmad

doi:10.32604/csse.2022.022269

Cited by 10 publications

(7 citation statements)

References 25 publications

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“…(43) r = 4.7913 and p = 2.7912 specify the solution to system of equations (43). Therefore, for with memory iterative technique ( 16)-( 18) the R-order of convergence is at least 4.7913.…”

Section: Note the Conditionmentioning

confidence: 99%

Two Novel With and Without Memory Multi-Point Iterative Methods for Solving Non-Linear Equations

Abdullah,

Choubey,

Dara

2024

Comm. Math. Appl.

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In this work, two new iterative methods are proposed for finding simple roots of non-linear equations. The new methods are the modifications of the existing work proposed by Rafiullah and Jabeen (New eighth and sixteenth order iterative methods to solve nonlinear equations, International Journal of Applied and Computational Mathematics 3 (2017), 2467 -2476). The first method obtained is of fifth-order two-step with memory method while the second scheme is three-point eight-order optimal without memory method. Firstly, the Hermite interpolation polynomial is employed to eliminate the first derivative. To maintain order, the conversion to a memory scheme was accomplished by introducing self-accelerated parameters, all without requiring any new function evaluations. Additionally, the Gauss quadrature approach was incorporated for the first derivative, aiming to attain optimal eighth-order convergence. In particular, the efficiency index is increased from 1.4953 to 1.7099 and 1.5157 to 1.6817 for fifth-and eighth-orders respectively. Some real-life applicationbased problems, such as Kepler's equation, an ocean engineering problem, Planck's radiation law, a blood rheology model, and the charge between two parallel plates were presented to validate and demonstrate the superiority of the proposed scheme. Another benefit of the proposed scheme is on the restriction of the Newton's method that f ′ (v) ̸ = 0 can be eliminated close to the root.

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“…(43) r = 4.7913 and p = 2.7912 specify the solution to system of equations (43). Therefore, for with memory iterative technique ( 16)-( 18) the R-order of convergence is at least 4.7913.…”

Section: Note the Conditionmentioning

confidence: 99%

Two Novel With and Without Memory Multi-Point Iterative Methods for Solving Non-Linear Equations

Abdullah,

Choubey,

Dara

2024

Comm. Math. Appl.

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“…Here, we present some examples to illustrate the performance and efficiency of MBHPM to solve TLDFSEs. CAS-Maple 18 with stopping criteria are used to terminate the computer program [42][43][44] :…”

Section: Numerical Outcomesmentioning

confidence: 99%

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Shams

Kausar

Khan

et al. 2023

Advances in Mechanical Engineering

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Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored.

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“…Problem 4 (blood rheology model [24]). The physical and flow characteristics of the blood are studied in the area of medical science called the blood rheology.…”

Section: Medical Science Models For Numerical Simulationsmentioning

confidence: 99%

“…Problem 6 (fluid permeability in biogels [24]). The relation of the pressure gradient to the fluid velocity in porous medium (extracellular fiber matrix) can be defined with the specific hydraulic permeability via the following nonlinear model:…”

Section: It Is Observed In Tablementioning

confidence: 99%

A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics

Qureshi

Soomro

Shaikh

et al. 2022

Computational and Mathematical Methods in Medicine

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This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton’s method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.

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Computer Oriented Numerical Scheme for Solving Engineering Problems

Cited by 10 publications

References 25 publications

Two Novel With and Without Memory Multi-Point Iterative Methods for Solving Non-Linear Equations

Two Novel With and Without Memory Multi-Point Iterative Methods for Solving Non-Linear Equations

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics

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