Numerical Application of Higher Order Linear Block Method for Solving Some Fourth Order Initial Value Problems

Raymond, D.; Kyagya, T. Y.; John, S.; Lydia, A.

doi:10.46481/asr.2023.2.1.67

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…The most common mathematical designed tools by some researchers includes numerical methods such as Euler method, Runge-Kutta (RK) method, Trapezoidal rule and Taylor series method, which are used to solve the first order IVPs. These numerical methods are also used to solve the higher order IVPs indirectly by reducing it to the first order system of equations [2][3][4][5][6]. However, this process is easy to implement but it will increase the number of equations as well as increase the cost for the process [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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On the Numerical Approximation of Higher Order Differential Equation

Zirra,

Skwame,

Sabo

et al. 2024

AJR2P

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This research examines the general K - step block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied. Some distinct fourth order oscillatory differential equation were directly applied on the new method in order to overcome the setbacks in reduction method, where the step size varies. The results obtained were compared with those in literature and the new method takes away the burden of solving fourth order oscillatory differential equations. The accuracy of the new method proved to be better as it outperformed those of existing methods. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantage of the new method is that it does not require much computational burden and it is also self-starting.

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Section: Introductionmentioning

confidence: 99%

“…Block method is capable of finding numerical solutions at more than a point at a time. [2,10] discourse the computational burden and zero-stability barrier in hybrid block method. The use of block hybrid method to approximate IVPs (1) directly is considered by some researcher in literature such as [3,7,[10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

On the Numerical Approximation of Higher Order Differential Equation

Zirra,

Skwame,

Sabo

et al. 2024

AJR2P

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“…An optimized half-step block method proposed in this article for solving (1) where some researchers applied the reduction method before adopting it. However, this process can only compute the numerical solution at one point at a time and time constraint [2,3]. Therefore, some scholars who newly applied the direct method to overcome the difficulties in reduction process in literature include [4,5,6].…”

Section: Introductionmentioning

confidence: 99%

An Optimized Half-Step Scheme Third derivative Methods for Testing Higher Order Initial Value Problems

et al. 2023

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An optimized half-step third derivative block scheme on testing third order initial value problems is presented in this article. This scheme suggests some certain points of evaluation which properly optimizes the truncation errors at point of formulas, the conditions that guarantee the properties of the method was considered and satisfied. However the develop scheme is used to test some third order optimized problems and the mathematical outcomes achieved confirms better calculation than the previous method we related with.

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Simulation of Two-Step Block Approach for Solving Oscillatory Differential Equations

John,

Ayinde,

Oyedepo

et al. 2024

Cumhuriyet Science Journal

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This study demonstrates the derivation of a two-step block scheme simulation through a linear block approach. The scheme's fundamental properties were thoroughly analyzed and found to fulfill all necessary conditions. The research focused on examining specific classes of oscillatory differential equations and comparing them to established methods. The findings indicate that the newly proposed methods exhibit superior accuracy and faster convergence compared to the existing methods investigated in this research. Consequently, the results highlight the improved precision and quicker convergence achieved with the new method. All computations were executed using Maple 18 software

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Numerical Application of Higher Order Linear Block Method for Solving Some Fourth Order Initial Value Problems

Cited by 3 publications

References 10 publications

On the Numerical Approximation of Higher Order Differential Equation

On the Numerical Approximation of Higher Order Differential Equation

An Optimized Half-Step Scheme Third derivative Methods for Testing Higher Order Initial Value Problems

Simulation of Two-Step Block Approach for Solving Oscillatory Differential Equations

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