7 research outputs found
A Computational Approach in Estimating the Amount of Pond Pollution and Determining the Long Time Behavioural Representation of Pond Pollution Model
This paper specifically develops a computational approach in estimating the amount
of pond pollution and determining the long time(every 48 hours) behavioural
representation of the pond pollution model.This approach, which can be considered as
an extension of the block predictor-corrector methods in form of implicit block
multistep method has many computational advantages usingvariable step size
technique. Moreover, it possesses some important advantages of designing a suitable
step size, stopping criteria(prescribed tolerance level) and error control/minimization
as well. This makes the new approach specifically efficient for solving systems of
first-order ordinary differentialequations. Analysis of some theoretical properties of
the method is carried out to ascertain the extent of performance of the method. Again,
numerical results are given to display the performance and efficiency of this new
method on system first-order ordinary differential equations
Multiprocessing Suited Pace Size Proficiency for Ciphering First Order ODEs
Abstract-Appraising computed error in forecasting-adjusting
system is all essential for purposeful acquiring suited pace size.
Diverse schemata for controlling/estimating error bank on
forecasting-adjusting system. This study examines
multiprocessing suited pace size (adaptive) proficiency for
ciphering first order ordinary differential equations (ODEs).
This involves compounding Newton’s back difference
interpolating multinomial with numeral consolidation method.
This is valuated at more or less preferred grid points to invent
multiprocessing forecasting-adjusting system. Moreover, process
progresses to produce main local truncation error (MLTE) of
multiprocessing forecasting-adjusting system after showing
degree of the system. Numeral resolutions manifest effectiveness
of varying pace size in working out first order ODEs.
Accomplished resolution rendered is aided using mathematical
software program. Mathematical resolutions show-case adaptive
proficiency is effectual and function better than subsisting
systems with respect to the maximal computed errors in the least
time-tested tolerance bounds
A Dilated Trigonometrically Equipped Algorithm to Compute Periodic Vibrations through Block Milne’s Implementation
This paper intends to investigate the use of a dilated trigonometrically equipped algorithm to compute periodic vibrations in block Milne's implementation. The block-Milne implementation is established by developing a block variable-step-size predictor-corrector method of Adam’s family using a dilated trigonometrically equipped algorithm. The execution is carried out using a block variable-step-size predictor-corrector method. This system has significant advantages that include the varying step-size and finding out the convergence-criteria and error control. Convergence-criteria and operational mode are discussed to showcase the accuracy and effectuality of the proposed approach
THE REVERSED ESTIMATION OF VARIABLE STEP SIZE IMPLEMENTATION FOR SOLVING NONSTIFF ORDINARY DIFFERENTIAL EQUATIONS
This study is design to examine the reversed estimation of variable step-size implementation for solving nonstiff ordinary differential equations. This is exclusively
dependent on the principal local truncation error of both predictor and corrector formulae of the same order. Collocation and interpolation methods with the aid of
power series as the approximate function is utilized in the construction of a class of predictor and corrector formulae of the same order with distinct. The computed results existed in literatures demonstrated the performance of the method over existing methods. The reversed estimation of predictor and corrector formulae is solely the predictor formulae and also, draws a lot of computational benefits which insures convergence, tolerance level, monitoring the step size and maximum errors
COMPUTING OSCILLATING VIBRATIONS EMPLOYING EXPONENTIALLY FITTED BLOCK MILNE’S DEVICE
Background and Objectives: The idea of estimating oscillating vibration problems via multinomial basis function haven been seen by some authors as a convenient
approach but not appropriate. This is as result of the behavior of the problem and as such depends largely on the step size and frequency. This research article is geared
towards computing oscillating vibrations employing exponentially fitted block Milne’s device (COVEFBMD). Materials and Methods: This is specifically designed using
interpolation and collocation via exponentially fitted method as the approximate solution to generate COVEFBMD, thereby finding the tolerance level of the method.
Results: Some numerical examples were selected and implemented on Mathematica kernel 9 to show speed, technicality and accuracy. Conclusion: The completed
solutions show that COVEFBMD performs better than the existing methods because of its ability to design a worthy step size; decide the tolerance level resulting to
maximized errors
A Dilated Trigonometrically Equipped Algorithm to Compute Periodic Vibrations through Block Milne’s Implementation
This paper intends to investigate the use of a dilated
trigonometrically equipped algorithm to compute periodic
vibrations in block Milne’s implementation. The block-Milne
implementation is established by developing a block variablestep-size predictor-corrector method of Adam’s family using a dilated trigonometrically equipped algorithm. The execution is carried out using a block variable-step-size predictor-corrector method. This system has significant advantages that include the varying step-size and finding out the convergence-criteria and error control. Convergence-criteria and operational mode are discussed to showcase the accuracy and effectuality of the proposed approach
Expanded Trigonometrically Matched Block Variable-Step-Size Technics for Computing Oscillating Vibrations
The expanded trigonometrically matched block
variable-step-size technics for computing oscillatory vibrations
are considered. The combination of both is of import for
determining a suited step-size and yielding better error estimates.
Versatile schemes to approximate the error procedure bank on
the choice of block variable-step-size technics. This field of study
employs an expanded trigonometrically matched block variablestep-
size-technics for computing oscillating vibrations. This
expanded trigonometrically matched is interpolated and
collocated at some selected grid points to form the system of
equations and simplifying as well as subbing the unknowns
values into the expanded trigonometrically matched will produce
continuous block variable-step-size technic. Valuating the
continuous block variable-step size technics at solution points of
will lead to the block variable-step-size
technics. Moreover, this operation will give rise to the principal
local truncation error (PLTE) of the block variable-step-size
technics after showing the order of the method. Numeral final
results demonstrate that the expanded trigonometrically
matched block variable-step-size technics are more
efficient and execute better than existent methods in terms
of the maximum errors at all examined convergence
criteria. In addition, this is the direct consequence of
designing a suited step-size to fit the acknowledged
frequence thereby bettering the block variable-step-size
with controlled errors