Anyone have a suggestion or comment about my sentence, please leave your idea. Actually I want to change this sentence to be more easier to understand for reader.

"Ordinary differential equations play an extremly important and useful role in applied mathematics, engineering and physics. In most real world phenomena, the ordinary differential equation that model the problem usually in nonlinear differential equations that cannot be solved using analytic technique. Therefore, numerical methods are usually required."

thank you~

"Ordinary differential equations play an extremly important and useful role in applied mathematics, engineering and physics. In most real world phenomena, the ordinary differential equation that model the problem usually in nonlinear differential equations that cannot be solved using analytic technique. Therefore, numerical methods are usually required."

thank you~

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Comments

a key rolein applied mathematics, engineering and physics. In mostreal-worldphenomena, ordinary differential equationsusually modelthe problem in nonlinear differential equations that cannot be solved using analytictechniques, sonumerical methods are usually required.I don't understand what's going on, but I think I've got the sentence simplified.Mister MicawberOrdinary differential equations (ODEs) play a key role in applied mathematics, engineering and physics. In most real-world phenomena, ODEs usually model the problem in nonlinear differential equations that cannot be solved using analytic techniques.

Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical methods are ussually required in order to approximate the solution of ODEs.I think this sentence is quite messy, may you give any idea to make this sentence easily understood ..thank you~

myviAre you saying that nonlinear differential equations

areorare notthe same as ordinary differential equations?I don't think this is made clear. You seem to be saying that one kind of equation models problems by using another kind of equation. This doesn't make sense. It's like saying that dotted lines on a map represent territories by using solid lines. You can't have it both ways.

CJ

CalifJimactually this is part of my thesis abstract.

myviI have underlined the grammar errors. I leave the examination of meaning to CJ:Ordinary differential equations (ODEs)

isa mathematical modelsthat play a key role in modelling real-world problems. This applicationcouldbe seen in physics, engineering, chemistry, biology and astronomy. The transformation of real-world problems intoa mathematical equationsarefor analysing and givinga solutionsviaan appropriate techniques. In many applications,ODEs usuallyin the form of nonlinear differentialequationthat cannot be solved using analytic techniques. Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical approximation techniques area powerful toolgivingthe solutions wedesiredMister MicawbermyvimyviOrdinary differential equations (ODEs) play a key role in modelling real-world problems such as are seen in physics, engineering, chemistry, biology, and astronomy. In many applications where real-world problems are transformed into mathematical equations, ODEs take the form of nonlinear differential equations that cannot be solved using analytic techniques. There is therefore a need for different methods for treating such problems efficiently and obtaining the desired solutions. Numerical approximation techniques are a powerful tool for meeting this need.

CJ

CalifJim