Fudziah Ismail
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View article: Influence of wetting-drying cycles on crack behaviour in fine soils: An experimental study
Influence of wetting-drying cycles on crack behaviour in fine soils: An experimental study Open
Desiccation characterised by extreme drying, poses significant challenges to the stability of structures like dams, particularly those constructed on fine-grained soils. Extensive crack propagation in these soils can significantly compromi…
View article: Adsorption of Malachite Green Using Rice Husk-Based Adsorbents
Adsorption of Malachite Green Using Rice Husk-Based Adsorbents Open
View article: Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions
Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions Open
In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary diff…
View article: A New Fractional Eg Modified Aor (Fegmaor) Method with Shifted Grünwald Estimate for the Solution of the Fractional Poisson Equation
A New Fractional Eg Modified Aor (Fegmaor) Method with Shifted Grünwald Estimate for the Solution of the Fractional Poisson Equation Open
View article: Numerical solution of third-order Robin boundary value problems using diagonally multistep block method
Numerical solution of third-order Robin boundary value problems using diagonally multistep block method Open
This numerical study exclusively focused on developing a diagonally multistep block method of order five (2DDM5) to get the approximate solution of the third-order Robin boundary value problems directly. The mathematical derivation of the …
View article: Formulation of a New Implicit Method for Group Implicit BBDF in Solving Related Stiff Ordinary Differential Equations
Formulation of a New Implicit Method for Group Implicit BBDF in Solving Related Stiff Ordinary Differential Equations Open
This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipul…
View article: Direct Solution of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si18.svg"><mml:mrow><mml:msup><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>″</mml:mo></mml:mrow></mml:msup><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:math>Using Three Point Block Method of Order Eight with Applications
Direct Solution ofUsing Three Point Block Method of Order Eight with Applications Open
This study aims to construct an implicit block method with three-point to tackle general second-order ordinary differential equations (ODEs) directly. Hermite Interpolating Polynomial is used as the fundamental function to obtain the propo…
View article: Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with Applications
Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with Applications Open
Recently, direct methods that involve higher derivatives to numerically approximate higher order initial value problems (IVPs) have been explored, which aim to construct numerical methods with higher order and very high precision of the so…
View article: Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application
Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application Open
This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorpor…
View article: Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems
Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems Open
In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent…
View article: A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$
A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$ Open
This paper deals with the derivation of an explicit two-stage thirdorder Improved Runge-Kutta Nyström (IRKNG) method for directly solving general second order ordinary differential equations (ODE).This method is twostep and the number of f…
View article: New explicit group modified accelerated overrelaxation (EGMAOR) in the solution of stationary partial differential equations
New explicit group modified accelerated overrelaxation (EGMAOR) in the solution of stationary partial differential equations Open
This research studies the Modified Accelerated Overrelaxation (MAOR) scheme on Stationary two-dimensional (2D) Partial Differential Equations (PDEs). The PDEs are discretized using the five-point Explicit Group (EG) finite difference metho…
View article: Direct Integration of Boundary Value Problems Using the Block Method via the Shooting Technique Combined with Steffensen’s Strategy
Direct Integration of Boundary Value Problems Using the Block Method via the Shooting Technique Combined with Steffensen’s Strategy Open
This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed bou…
View article: Numerical solution to Volterra Integro-Differential Equations of the second kind by hybrid one-step block method
Numerical solution to Volterra Integro-Differential Equations of the second kind by hybrid one-step block method Open
The hybrid block one-step method of order four is presented and implemented to solve first order Volterra Integro-Differential Equations (VIDEs). The technique is developed using Lagrange interpolation method. The numerical solutions of VI…
View article: An experimental study of the modified accelerated overrelaxation (MAOR) scheme on stationary helmholtz equation
An experimental study of the modified accelerated overrelaxation (MAOR) scheme on stationary helmholtz equation Open
This research aims to experiment the Modified Accelerated Overrelaxation (MAOR) scheme on second order iterative method for solving two dimensional (2D) Helmholtz Equation. The equation is discretized using the standard second order (Full …
View article: Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs
Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs Open
In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs).The method incorporates the first and second derivatives of f(x, y, y ), which are the third a…
View article: Fuzzy Volterra Integro-Differential Equations Using General Linear Method
Fuzzy Volterra Integro-Differential Equations Using General Linear Method Open
In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method an…
View article: Explicit Integrator of Runge-Kutta Type for Direct Solution of u(4) = f(x, u, u′, u″)
Explicit Integrator of Runge-Kutta Type for Direct Solution of u(4) = f(x, u, u′, u″) Open
The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u ( 4 ) = f ( x , u , u ′ , u ″ ) and denoted …
View article: Two and three point implicit second derivative block methods for solving first order ordinary differential equations
Two and three point implicit second derivative block methods for solving first order ordinary differential equations Open
In this research we developed implicit block methods which make used of the first and second derivatives of the problems.The aim is to give a more accurate as well as faster numerical results for solving first order ordinary differential e…
View article: Numerical solutions of Volterra integro-differential equations using General Linear Method
Numerical solutions of Volterra integro-differential equations using General Linear Method Open
In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and 'roo…
View article: Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation
Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation Open
In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first …
View article: Exponentially-fitted forth-order explicit modified Runge-Kutta type method for solving third-order ODEs
Exponentially-fitted forth-order explicit modified Runge-Kutta type method for solving third-order ODEs Open
In this paper exponentially-fitted explicit modified Runge-Kutta type method denoted as EFMRKT for solving y'''(x) = f(x, y, y') is derived. The idea presented is based on the Simos and Berghe approach which exactly integrates initial valu…
View article: Numerical solution for stiff initial value problems using 2-point block multistep method
Numerical solution for stiff initial value problems using 2-point block multistep method Open
This paper focuses on the derivation of an improved 2-point Block Backward Differentiation Formula of order five (I2BBDF(5)) for solving stiff first order Ordinary Differential Equations (ODEs). The I2BBDF(5) method is derived by using Tay…
View article: Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions
Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions Open
This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs) with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained d…
View article: Solving Oscillatory Delay Differential Equations Using Block Hybrid Methods
Solving Oscillatory Delay Differential Equations Using Block Hybrid Methods Open
A set of order condition for block explicit hybrid method up to order five is presented and, based on the order conditions, two-point block explicit hybrid method of order five for the approximation of special second order delay differenti…
View article: Block Hybrid Method with Trigonometric-Fitting for Solving Oscillatory Problems
Block Hybrid Method with Trigonometric-Fitting for Solving Oscillatory Problems Open
In this paper, we develop algebraic order conditions for two-point block hybrid method up to order five using the approach of B-series.Based on the order conditions, we derive fifth order two-point block explicit hybrid method for solving …
View article: Exponentially Fitted and Trigonometrically Fitted Explicit Modified Runge-Kutta Type Methods for Solving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">′</mml:mi><mml:mi mathvariant="normal">′</mml:mi><mml:mi mathvariant="normal">′</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">′</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:math>
Exponentially Fitted and Trigonometrically Fitted Explicit Modified Runge-Kutta Type Methods for Solving Open
Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are li…
View article: Diagonally Implicit Multistep Block Method of Order Four for Solving Fuzzy Differential Equations Using Seikkala Derivatives
Diagonally Implicit Multistep Block Method of Order Four for Solving Fuzzy Differential Equations Using Seikkala Derivatives Open
In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solvin…
View article: Numerical simulation of fuzzy differential equations using general linear method and B-series
Numerical simulation of fuzzy differential equations using general linear method and B-series Open
In this article, numerical simulation of fuzzy differential equations using general linear method is proposed. The significance of general linear method is derivation of algebraic order conditions of method using technique of rooted trees …
View article: THE POINT WISE BEHAVIOR OF 2-DIMENSIONAL WAVELET EXPANSIONS IN $L^p(R^2)$
THE POINT WISE BEHAVIOR OF 2-DIMENSIONAL WAVELET EXPANSIONS IN $L^p(R^2)$ Open
We show that the two dimensional wavelet expansion of Lᴾ (R²) function for 1 < p < ∞ converges pointwise almost everywhere under wavelet projection operator. This convergence can be established by assuming some minimal regularity to get th…